Question

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

Answer 1

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`