Question

What is the solution of log2x + 6 144 = 2?

Answer 1

2x+6 is the base

Then the equation is logarithm of 144 on basis 2x + 6 = 2

Then [2x + 6]^2 = 144

Now expand the square binomial

4x^2 + 24x + 36 = 144

4x^2 + 24x + 36 - 144 = 0

4x^2 + 24x - 108 = 0

Divide by 4

x^2 + 6x - 27 = 0

Factor: (x + 9 ) (x - 3) = 0

x = -9 and x = 3

The only valid is x = 3, because x = -9 yields 2x + 6 = - 12 and the logarithm function cannot have negative basis.

Then the answer is x = 3.