1. ## Logarithmic equation

Solve $\displaystyle \log_5 (x-4) = \log_7 x$ for x. Round the answer from your calculator to 4 decimal places.

This is a "Show your work" question. I don't understand what work can be shown here except for the final answer: x=11.5842

2. Originally Posted by Ivan
This is a "Show your work" question.
Well, then you had better start showing! What have you tried? Do you have the change of base formula?

For appropriate a, b, and c

$\displaystyle log_{b}(a) = \frac{log_{c}(a)}{log_{c}(b)}$

That should make you feel like you are doing something. Too bad it will not lead anywhere.

Since you must use iterative techniques to solve this, you should state what method you are using and then implement it carefully.

3. Can someone please do this question? I've tried some crazy stuff to try and work it out, all failed except one where I ended up using the Newton-Raphson method, which I think is too much work. Is there some easier way I am overlooking?

4. Originally Posted by Ivan
Solve $\displaystyle \log_5 (x-4) = \log_7 x$ for x. Round the answer from your calculator to 4 decimal places.

This is a "Show your work" question. I don't understand what work can be shown here except for the final answer: x=11.5842
I don't find an analytical solution yet (actually, I already quit to this), but try graphing each side, you'll find the solution.

5. Say,
$\displaystyle \frac{\log (x-4)}{A} = \frac{\log x}{B}$
Where $\displaystyle A,B>0$.

$\displaystyle 10^{\log(x-4)/A} = 10^{\log x/B}$

$\displaystyle (x-4)^{1/A} = x^{1/B}$

Thus,
$\displaystyle (x-4)^B = x^A$

There is no general analytic approach in general if $\displaystyle A\not = B$ and they are not integers.