How do you solve logx + log(x + 15) = 2?

1 Answer
Mar 21, 2016

Answer

Explanation:

logx+log(x+15)=2
log(x(x+15))=2

Here is the catch. This log can be from any base p. I assume this is log base 10. So
log_10(x^2+15x)=2
Taking antilog on both sides
x^2+15x=10^2
x^2+15x-100=0

Then factorize this to get the solution.

(x+20)\times(x-5) = 0
x = -20,5

Similar equations can be derived for various bases to get different solutions.

For general case the equation to solve is
x^2+15x-p^2=0
x = (-15\pmsqrt(225+4p^2))/2