0
votes
1answer
32 views

Find $t$ in $N = b \times g^t$.

The problem is the following: Find the value of $t$ in $N = b × g^t$. So for example "$512.000 = 2000 × 2^t$" I'm not really a mathematician so their may be a simple way or it could be hard.
0
votes
1answer
29 views

Prove this logarithm equation

I keep getting the wrong answer. Can someone please correct my working out a^x=b^(1-x) In(a)^x=In(b)^(1-x) xIn(a)=(1-x)In(b) xIn(a)=In(e)-xIn(b) xIn(a)+xIn(b)=In(e) x[In(a)+In(b)]=Ine ...
0
votes
1answer
39 views

Inverse Function of Logarithm

The answer is A but I don't understand why! $ -2 \log_e (x^2) $ can be re-written as $ -4 \log_e(x) $ right? but why do these two graphs look different? the graph $-2 \log_e (x^2) $ is one to ...
0
votes
1answer
14 views

Maximum value of constant in logarithm problem

The first thing I did was: make: (x-1)^2 - k > 0 (x-1)^2 > k don't know what to do after this point... the maximum value of k is 9 i dont really understand what the maximum value of k is? ...
1
vote
0answers
29 views

Interchanging from exponential form to log form

Shouldn't the answer be x = loge(everything else in the bracket) why is the loge function divided by "k" ???
1
vote
1answer
20 views

Sketching Logs with Quadratic Terms

$\log(x^2+1) = y$ asymptote at $x^2+1 > 0$ and so there is no asymptote $x$ and $y$ intercept at $(0,0)$ How do you know that the function goes both directions, and has a dip in the middle? ...
1
vote
1answer
62 views

(Basic High School Mathematics) Graphing the inverse square law

I did an experiment measuring the intensity of light in relation to the distance away from a source. How would I graph the avg intensity over 1/distance squared? Note that T1 = trial 1 etc.. It's ...
2
votes
7answers
116 views

for $n$ an integer, why is $n^0=1$ ??

This is so going to cost me.... I was wondering why for any integer $n$: $n^0 =1$. Perhaps It's because $n$ is a round number and if $m$ is a non negative integer, also round then: $$n^m = 1 \cdot ...
0
votes
1answer
30 views

Just one step away. Exponential formula

The data points are. I have worked out that. y =.032(2.5)^x is correct where my table is x = 0, y = .032 x = 1, y = .08 x = 2, y = .2 How do I get my formula to reflect y=-3, x =.0320 ...
0
votes
2answers
11 views

Calculating how many iterations to make a list that doubles each iteration, n elements long

If I have a list of numbers starting with four numbers, the list doubles in size after each iteration, how would I calculate how take to have a list of exactly n elements long? Thanks
0
votes
2answers
35 views

Proportionality to find spent years for price drop

Well, the title's kinda messy, but this is a concrete example of what I'm trying to find out: Lets say there is a price of 40.000 USD, if the price drops at half, how many years does it take for the ...
1
vote
1answer
47 views

If$ a+b-1=1+\frac{ln(2^a-1)}{ln4}+\frac{ln(2^b-1)}{ln4}$ then $a=b$?

If $$a+b-1=1+\frac{ln(2^a-1)}{ln4}+\frac{ln(2^b-1)}{ln4}$$ where $a,b>0$ are real numbers and ln is $log_e$, then is a=b?
4
votes
1answer
83 views

Proof of $e^{\ln(x)\ln(2)}$, which natural logarithm do I bring down?

I'm currently stumped with the proof for the following problem: $$F(x) = 2^{\ln(x)}$$ $$\Rightarrow F(x) = y$$ $$y = 2^{\ln(x)}$$ $$\ln(y) = \ln(2^{\ln(x)})$$ $$\ln(y) = \ln(x)\cdot\ln(2)$$ $$y = ...
1
vote
2answers
50 views

How can I solve the equation…

$$\log\left(\frac{\pi_i}{1-\pi_i}\right)=\sum_{k=0}^K x_{ik}\beta_k\qquad i=1,2,\dots,N$$ How can I make the equation above the one below by taking "$e$" to both sides. Note that after taking $e$ ...
0
votes
1answer
38 views

How to solve this equation with linear n as well as polynomial n?

I am banging my head against the wall, but somehow I can't find a closed form solution to this equation in n: $$229,244 + 58,044 \cdot n = 130,000 * 1.78^n$$ Obviously, if there was no $n$ ...
0
votes
1answer
81 views

Exponential equation+derivative

I saw here on math.stackexchange.com an equation which has very nice solutions (by solutions I mean a proof): $3^x+28^x=8^x+27^x$, where $x$ is a real number. However, I think there must be an ...
0
votes
1answer
350 views

Compound interest formula and continuously compounded interest formula derivation

My textbook gives the formula for compound interest as: $A\left( t\right) =P\left( 1+\dfrac {r}{n}\right) ^{nt}$ Where: P = The principal, r=the annual rate of interest, n= the frequency of ...
-2
votes
1answer
51 views

How come is this equals to 1??

How is this equal to $1$.. $e^{-i}(\frac{2·\pi·k·(-N)}{N})=1$ ??? http://cnx.org/content/m12024/latest/#Boncelet
0
votes
4answers
36 views

Exponential Growth

A colony if bacteria in a petri dish grows exponentially. At noon, there 1000 bacteria cells in the dish. At 8 pm, there 3000 cells in the dish. How long does it take the bacteria to double its ...
2
votes
3answers
303 views

Solve $2^{x}=x^{2}$

I've been asked to solve this and I've tried a few things but I have trouble eliminating x. I first tried taking the natural log: $x\ln \left( 2\right) =2\ln \left( x\right) $ $\dfrac {\ln \left( ...
0
votes
1answer
59 views

Solve the inequality $2^{\left( x^{3}-x\right) } < 1$

$2^{\left( x^{3}-x\right) } < 1$ Let $2^{\left( x^{3}-x\right) }-1=f\left( x\right)$ To find the values for which $f(x)<0$ I let $f(x)=0$: $2^{\left( x^{3}-x\right) }-1=0$ $2^{\left( ...
0
votes
3answers
35 views

Why do I receive the wrong answer when I try to solve this exponential equation?

So I have the equation: $25^{x}=5^{x}+6$ My reasoning is if you make everything to the base 5: $\left( 5^{2}\right) ^{x}=5^{x}+5^{\log _{5}6}$ Given the bases are the same we can do: $2x=x+\log ...
5
votes
2answers
180 views

Solving $x^2 - 1 = e^x$

Can someone help me solve the equation $x^2 - 1 = e^x$ ? I tried taking the natural logarithm of both sides but I don't know where to go from there.. I got: $\ln(x^2 -1) = x$ But I don't know how ...
1
vote
1answer
29 views

Help needed clearing up a textbook explanation of logarithms

A passage in my textbook has me confused, first it states this: $ \log _{a}\left( x\right) .\log _{b}\left( a\right) =\log _{b}\left( a^{\log _{a}\left( x\right) }\right) =\log _{b}\left( x\right) $ ...
1
vote
8answers
313 views

Given $2^{x}=129$, why is it that I can use the natural logarithm to find $x$?

I've looked at an example in my textbook, it is: $2^{x}=129$ $\ln \left( 2^{x}\right) =\ln \left( 129\right) $ $x\ln \left( 2\right) =\ln \left( 129\right) $ $ x=\dfrac {\ln \left( 129\right) ...
1
vote
2answers
94 views

Confusion regarding the Logarithmic function change of base formula

My textbook seems to be making a big leap when trying to prove the change of base formula for logarithms. If someone could help clear this up it would be very appreciated. It starts with: $b^{x ...
1
vote
1answer
59 views

How is the gradient of exponential functions with different bases (in the included table) worked out?

I am studying exponential functions at the moment, and this table was presented in my textbook to show that for exponential functions with increasing 'bases' the gradient of the function increases. ...
0
votes
1answer
75 views

Practical significance of $e$ [duplicate]

We know, for example, the constant $\pi$ is the perimeter of a circle with diameter $1$ unit. In the similar manner how would we explain the constant $e$. I have searched a lot for it. But I couldn't ...
3
votes
2answers
108 views

Why is it important to define that a logarithm and exponential function is one-to-one?

I'm currently studying the properties of logarithm in an open source pre-calculus textbook that can be found here (Page 438). Before the text goes on to the Algebraic properties of exponential and ...
0
votes
2answers
39 views

Exponent multiplication error

$\left( x^{2/3}\right) ^{3/2}=x^{\dfrac {2}{3}\times \dfrac {3}{2}}=x^{1}$ Given this why is it that if I substitute $x=-1$ I get 1?: $\left( \left( \sqrt [3] {-1}\right) ^{2}\right) ...
2
votes
1answer
71 views

Trouble solving polynomial equation with exponent

I'm having trouble solving this equation.It looks simple, but I just can't find the answer.Can someone help me? $$9x^4-13x^2+4 = 0$$
2
votes
2answers
51 views

Changing an exponential function to logarithmic

I have a question stating that $P=75e^{-0.005t}$ and they want to get t by itself. I used the example $y=2^x = x=log_2(y)$ To find that $-0.005t = 75ln(P)$ So $t=\frac{75ln(P)}{-0.005}$ However ...
0
votes
1answer
49 views

You can write ${\left( {\frac{1}{2}} \right)^x}$ as ${2^{ - x}}$ , can the same be done with ${\left( {\frac{2}{3}} \right)^x}$?

You can write ${\left( {\frac{1}{2}} \right)^x}$ as ${2^{ - x}}$ as: ${\left( {\frac{1}{2}} \right)^x} = {({2^{ - 1}})^x} = {2^{ - x}}$ But what about ${\left( {\frac{2}{3}} \right)^x}$? Can it be ...
3
votes
1answer
184 views

Help find the derivative of $e^{2^x}$ using the definition of the derivative

Let $f(x) = e^{2^x}$, where $e$ is the exponential function. So the $f'(x)$ is: $\begin{align}f'(x) &=& \lim_{h \to 0} \frac{e^{2^{x+h}}-e^{2^x}}{h}\\ &=& ...
2
votes
2answers
38 views

How do I prove a “double limit”?

Prove $$\lim_{b \to \infty} \lim_{h \to 0} \frac{b^h - 1}{h} = \infty$$ I have never worked with double limits before so I have no idea how to approach the problem. Please don't use "$e$" in your ...
0
votes
2answers
130 views

How do I solve this exponential function? $2^{-100x} = (0.5)^{x-4}$

How do I solve for $x$? $2^{-100x} = (0.5)^{x-4}$
2
votes
1answer
215 views

Exponential Function Shifts

I have some confusion about shifts concerning exponential functions. I can best describe my question with an example. Take y = e^-(x-3). This graph has a reflection over the y-axis and is shifted ...
0
votes
0answers
54 views

Solution for a Mixture of Two Exponential Equations

I have a survival function that is a combination of two exponential functions. I would like to solve for the median survival time (ie when half the population is dead). $$0.5 = \left( A(0) + A(0) ...
0
votes
1answer
554 views

Problem to find the intersection of a exponential and linear function

I have the problem to find the intersection of a exponential and linear function. My math teacher can't help me, but I'm interested how I can solve this. I tried to use the equating method, but it ...
6
votes
6answers
398 views

Why is $ \sum_{n=0}^{\infty}\frac{x^n}{n!} = e^x$?

I am trying to see where this relationship comes from: $\displaystyle \sum_{n=0}^{\infty}\frac{x^n}{n!} = e^x$ Does anyone have any special knowledge that me and my summer math teacher doesn't know ...
5
votes
3answers
382 views

Solve an equation with $e^{(x-2)}=e^{4}\cdot e^{\sqrt{x}}$

$$e^{(x-2)}=e^{4}e^\sqrt{x}$$ I know that $x = 9$ and I can show the calculations like this: $$e^{(x-2)} = e^{\sqrt{x}+4}$$ and now I need to get the $x$ to the right side but I dont know how.
1
vote
1answer
329 views

Normalizing an exponential function

Given the equation $a^\frac yx + a^x=b$ is there a way to normalize this function into a form where $y=$...? In short can I express $y$ in terms of $x$ if $a$ and $b$ are constants?
2
votes
3answers
109 views

Show that $x=2\ln(3x-2)$ can be written as $x=\frac{1}{3}(e^{x/2}+2)$

Show that $x=2\ln(3x-2)$ can be written as $x=\dfrac{1}{3}(e^{x/2}+2)$. Is there a rule for this?
5
votes
1answer
63 views

Do we really know the value of expressions with irrational powers?

The way we evaluate decimal powers such as $a^.75$ is by splitting it into $(a^3)$^(1/4). How then can we evaluate irrational powers? I know that we can approximate, but whenever we graph a^x we ...
1
vote
1answer
87 views

Solving basic exponential equation with logs

I am having trouble with this grade 12 pre-calc question that I am sure will be elementary to most of you. I understand most of it but I do not understand one of the steps. These are the steps in my ...
1
vote
0answers
63 views

Finding the zeroes of finite exponential sum

I want to find the zeroes for functions that look like this (an example): $f(t) = k_1e^\left(a_1t\right)+k_2e^\left(a_2t\right)+k_3e^\left(a_3t\right)$ Where all a are negative real numbers, so this ...
9
votes
4answers
228 views

prove that $\frac{1-e^{-x^2}}{x}\le 2\sqrt{2} , \ x>0$,

Can you show very easy methods? I hope I'll see many methods. Thank you everyone. Prove that: $$\frac{1-e^{-x^2}}{x}\le 2\sqrt{2} \ \ \ \qquad \forall x>0.$$
1
vote
1answer
202 views

Stuck on solving for x in exponential to find variance

The problem seems simple: Let X be an exponential random variable such that $P(X \le 2) = 2P(X > 4)$. Find the variance of X. Easy, right? $ P(x \le 2) = 1 - e^{-2\lambda} $ and $ P(x > 4) = ...
0
votes
1answer
129 views

upper bound for $e^{ax^2}$

I want to find a upper bound for $$e^{ax^2}\leqslant \: ?$$ "a" is a constant and $a\geqslant 0$ . x is a variable. I prefer to have a polynomial function or power function (like $ x^{k}$) is there ...
0
votes
2answers
61 views

Solving exponential (decay) for x

Well seems like I have a mathematical breakdown at the moment.. But I'm wondering, how CAN you actually solve a function of the form $y = y_0 + Ae^{Bx} + Ce^{Dx}$ (Where B & D are negative, non ...