0
votes
1answer
25 views

Stuck on derivative of logarithm of sum of exponentials

let's say that I need to calculate the following expression: $$ \frac{\partial\mathrm{log}(\mathrm{exp}(w_1 * x_1 + b_1) + \mathrm{exp}(w_2 * x_2 + b_2))}{\partial w_1} $$ How do I start? The rules ...
2
votes
2answers
29 views

Can the following equations be solved without the need of numerical methods?

I'm taking advanced algebra in school. I have been asked to solve two equations: $\log_{6}(1-x) + \log(x^{2}-9) = 2 \\$ $ 3^{x+2} + 2^x = 5 $ The teacher said this equations can be solved ...
0
votes
3answers
71 views

How would you solve for $x$ in $7^{x}=5^{x-4}$?

How would you be able to make these the same base? I tried to put it into a base $10$ formula, but it ended up making $x=0$.
3
votes
1answer
432 views

How to find a summation of a logarithmic function?

Suppose that I had to find $\log_{10}(8952!)$. Now, since $\log(a) + \log(b) = \log(ab)$, this can be rewritten to the following summation: $$\sum_{x=1}^{8952}{\log_{10}(x)}$$ Would there be a ...
1
vote
1answer
90 views

What is the $\sum\limits_{i=0}^{\ (\log_2(n))-1)}\frac{n}{2^i}$?

What is the value of the following sum: $$\sum\limits_{i=0}^{\ (\log_2(n))-1)}\frac{n}{2^i}$$ Can you show how to go about arriving at the answer?
0
votes
1answer
35 views

Specific range of numbers is given, trying to get another number within same range

I'm trying to calculate the width of an HTML element based on the window size. Here's what I have. These width values (first value) accurately match with the width the HTML element must be (second ...