0
votes
2answers
37 views

Solving equations having both log and exponential forms

How can one Solve equations having both log and exponential forms: For eg... $e^x$ $=$ $\log_{0.001}(x)$ gives $x=0.000993$ (according to wolfram-alpha ...
3
votes
1answer
55 views

Solving exponential equation $e^{x^2+4x-7}(6x^2+12x+3)=0$

How would you find $x$ in: $e^{x^2+4x-7}(6x^2+12x+3)=0$ I don't know where to begin. Can you do the following? $e^{x^2+4x-7}=1/(6x^2+12x+3)$ and then find $ln$ for both sides?
0
votes
1answer
13 views

Explicit and Recursive Exponential Growth

The population of a certain organism triples every hour. Write a function that models this growth. By what factor does the population grow in one-half hour? I'm unsure of how I should approach the ...
3
votes
4answers
75 views

Exponential equation: $2e^{-x} - e^{-2x}=0.$ [closed]

$2e^{-x} - e^{-2x}=0.$ the correct answer is $x=-\ln2$. How do I get there?
2
votes
2answers
61 views

Solve the inequality $(1/2)^x-(1/2)^{-1-x}\ge1$ for real $x$

I have to solve in $\Bbb{R}$ the following inequality : $$ \left(\frac{1}{2}\right)^{x} - \left(\frac{1}{2}\right)^{-1 - x} \ge 1 \qquad(E) $$ So far I have : For $x=0$ this inequality if not ...
1
vote
4answers
89 views

How many solutions $k>1$ does the equation $\exp ((k-1)/( k+1))=\sqrt{k}$ have?

I have the following equation: $e^{\frac{k-1}{k+1}}=\sqrt{k}$. The question is: how many solutions does it have? ($e$ is Euler's constant and k is a positive real number >1).
2
votes
4answers
137 views

Solving the power equation $A^X = \frac{(1+X)}{(1-X)}$

I want to solve the following power equation (get $X$ value): $$A^X = \frac{(1+X)}{(1-X)},$$ where $X\neq 0$, $A\in {\mathbb R}$ (a real number) $$A \geq 0 , \quad A \leq 1$$ I think $X$ should be ...
1
vote
2answers
67 views

Neither $\log x$ nor $\exp(x)$ are rational functions [closed]

(a) Prove that $\log x$ cannot be expressed in the form $f(x)/g(x)$ where $f(x)$ and $g(x)$ are polynomials with real coefficients. (b) Prove that $e^x$ cannot be expressed in the form $f(x)/g(x)$ ...
2
votes
4answers
41 views

Number of distinct real roots with $e^{-x}$ in the equation

How to find the number of distinct real roots of the equation $$13x^{13}-e^{-x}-1=0$$ I know that we generally find number of real roots by observing number of sign changes in $f(x)$ and $f(-x)$ but ...
0
votes
1answer
32 views

Solve for coefficients of $y = A(1 - e^{-x/B})$ given two points

I have the equation $y = A(1 - e^{-x/B})$, and two $(x,y)$ pairs. How can I solve for $A$ and $B$? This should be simple, but I've been banging my head against the algebra for a while to no avail. I ...
3
votes
2answers
145 views

Exponential function to logarithmic function

i'm stuck on completing this equations. Is this correct? $$z=a e^{-bt}$$ $$\ln(z)=\ln(a)+\ln(e^{-bt})$$ $$\ln(z)=\ln(a)+(1)(-bt)$$ $$\ln(z)=\ln(a)-bt$$
0
votes
1answer
21 views

Graph exponential function

I am having problems understanding why $xe^x + 10e^x$ has two $(x,y)$ intercepts. I understand why there is one $(0,10)$, but am unclear on how to return $(-10,0)$. Any help would be much ...
3
votes
2answers
60 views

What is the domain of $x^x$

I'm trying to figure out the domain of the function $y=x^x$. When I graph it, it appears to be defined on $[0, \infty)$, but then when I plug in individual negative numbers, for some of them I get ...
1
vote
0answers
71 views

Only one positive solution

When $(a+b)^2=(x-3a)(x-b)e^x$ has only one positive solution, find the relationship between a and b. Here, a and b are constants and satisfy $a>b>0$. Hint: consider the graph of ...
1
vote
1answer
18 views

Derivative of exponential function

1) $f(t) = (\ln 5)^t$ what is the $f'(t)$? I tried $t\ln(5)$ but it was wrong. 2) $f(x) = x^{\Large π^6} + (π^4)^x$ This one I did not attempt in it because I find it confusing little bit.
1
vote
1answer
40 views

A problem with progressive percentage incrementation

I have absolutely no clue if any of the terms I used in the title actually exist or make sense. I'm usually good at math (relatively) but I am facing this problem today that I just cannot solve. John ...
0
votes
3answers
48 views

Exponential problem

$\$10,000$ increases every day by $1\%$. How long until it doubles? I tried doing it by multiplying by $1\%$ for each day and got $10$ days but I don't think that is right. I know there must be an ...
0
votes
1answer
69 views

What is the outdoor temperature? Working included.

Is my working correct in regards to this question? I'm quite stuck on it and I'm not too sure if I am in the right direction. Any advice is appreciated. Thank you. Question: A thermometer that has ...
1
vote
1answer
58 views

Is my working correct? Exponenial decay

Is my working correct? If not, please let me know where I have gone wrong. Thank you for taking the time to check! Question: A thermometer that has been stored indoors where the temperature is 22 ...
3
votes
1answer
114 views

Is the function $f(x)=1^x=1$ considered an exponential function?

I am confused about the following: The exponential function (by definition) is a function of the form $f(x)=a^x$ where $a>0$. However, when $a=1$, we get the constant function $f(x)=1^x=1$. Is the ...
0
votes
1answer
74 views

What is the outdoor temperature? Help please!

Does anyone know how I would go about answering this question? Any feedback is appreciated! A thermometer that has been stored indoors where the temperature is 22 degrees Celsius, is taken outdoors. ...
0
votes
2answers
51 views

Compound interest coumpounded n time per year formula. $A=P\left(1+\frac{r}{n}\right)^{nt}$ intuition behind it.

I know that the compound interest formula for the interest compounded annually is given by $$A=P(1+r)^t$$ I know the intuition behind it. But why the compound interest formula for the interest ...
1
vote
1answer
47 views

Exponential problems

A ship embarked on a long voyage. At the start of the voyage, there were 300 ants in the cargo hold of the ship. One week into the voyage, there were 600 ants. Suppose the population of ants is an ...
1
vote
1answer
71 views

Solving Exponential Function for termites vs spiders

The populations of termites and spiders in a certain house are growing exponentially. The house contains 120 termites the day you move in. After four days, the house contains 210 termites. Three days ...
1
vote
2answers
31 views

Exponential Growth Rates

So if you are given two different numbers to determine a growth rate, do you use to largest number compared to the value when x=0. For example the problem I am working on is: Your grandfather ...
4
votes
3answers
76 views

Game With 21 Squares, How Many Possible Answers? Function Building

We played this game in our math class, okay, I'll explain how it's played. There are 21 squares in a straight line across, the first person shades in 2 adjacent squares. The next player shades in 2 ...
2
votes
2answers
21 views

Exponential growth precalc population

The population of City A increases by 8% every 10 years. The population of City B triples every 120 years. The two cities had equal populations of 10,000 residents each in the year 2000. In what year ...
0
votes
1answer
34 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
35 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
46 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
17 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
33 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
26 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
97 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
129 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 ...
-1
votes
1answer
34 views

Rearranging the terms so that the denominator becomes the numerator

I have the equation $$ \frac{120}{1 + 3.167 \cdot e^{-0.05t}} = 60 $$ How do I transform it so that the denominator becomes the numerator? This would make the problem much easier.
2
votes
1answer
67 views

How to solve $6^{2x}-10\cdot 6^x=-21$ using logarithms?

What do I do with $\large 6^{2x}-10\cdot 6^x=-21$? Since $6$ and $-60$ are not of the same base (nor can they be written as exponents of the same base cleanly) I am having trouble solving for ...
0
votes
1answer
36 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
13 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
6answers
109 views

How to find all solutions of $4^x-3^x=1$?

I have problem with equation: $4^x-3^x=1$. So at once we can notice that $x=1$ is a solution to our equation. But is it the only solution to this problem? How to show that there aren't any other ...
0
votes
2answers
37 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
101 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
54 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
40 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
89 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
3k 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 ...
-1
votes
1answer
57 views

How come is this equals to 1?? [closed]

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
46 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
308 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( ...