# Thread: Logarithmic equation with different bases

1. ## Logarithmic equation with different bases

Would appreciate some guidance on the problem below:

Solve Log[base 25](6x + 25) + Log[base 5](x + 25) = 5, x a Natural number

To solve I tried converting to a single base using Log[base A]x = Log[base B]x / Log[base B]A which gives:

Log[base 25](6x + 25) = Log[base 5](6x + 25) / Log[base 5]25 = Log[base 5](6x+25) / 2

So the equation becomes:

Log[base 5](6x + 25) / 2 + Log[base 5](x + 25) = 5

Log[base 5](6x + 25) + 2Log[base 5](x + 25) = 10

Log[base 5](6x + 25) + Log[base 5](x + 25)^2 = 10

Log[base 5](6x + 25)(x + 25)^2 = 10

5^10 = (6x +25)(x +25)^2

This seems like a nasty polynomial to solve - is there a simpler approach to the problem?

Corbomite1

2. ## Re: Logarithmic equation with different bases

No that is exactly what you have to do.

OK, thanks!

4. ## Re: Logarithmic equation with different bases

Originally Posted by corbomite1
Would appreciate some guidance on the problem below:
Solve Log[base 25](6x + 25) + Log[base 5](x + 25) = 5, x a Natural number
Here is some advice on notation.
You can learn to post symbols. It really is so easy. And it makes most of us more willing to find out how to help.
This subforum will help you with the code. Once you begin, you quickly learn the code.

[TEX]\log_{25}(6x+25)+\log_{5}(x+25)=5 [/TEX] gives $\log_{25}(6x+25)+\log_5(x+25)=5$
If you click on the “go advanced tab” you should see $\boxed{\Sigma}$ on the tool-bar. That gives the [TEX]..[/TEX] wrap. Your LaTeX code goes between them.

5. ## Re: Logarithmic equation with different bases

Understood, will do, thanks!

So the problem would read $\log_{25}{(6x+25)} + log_5{(x+25)}=5$