Question

How do you solve `log_2( 2x) + log _ 2 x = 5`?

Answer 1

I found `x=4`

Explanation:

We can use the property of logs relating the sum with the product of the arguments and write:
`log_2(2x*x)=5`
use the definition of log:
`2x^2=2^5`
`x^2=32/2`
`x=+-sqrt(16)=+-4`
only the positive one is acceptable.