Question

Consider the equation below. log4 (x+3)=log2 (2x). Which system of equations can represent the equation?

Answer 1

Full problem. The reason people can't answer the question is because ya'll don't post all the information.

Answer 2

Note that

`log_(4) (x+3) = (log_(2) (x+3))/(log_(2)4)`

Therefore, given
log₄(x+3) = log₂(2x), obtain

`(log_(2)(x+3))/(log_(2)4)=log_(2) (2x) \\ log_(2)(x+3) = log_(2)4 log_(2)(2x) \\ x+3 = (2x)^{log_(2)4}`
Because
log₂4 = log₂ 2² = 2 log₂ 2 = 2, therefore
x + 3 = (2x)² = 4x²
4x² - x - 3 = 0
This factorizes into
(4x + 3)(x - 1) = 0

Answer:
4x² - x - 3 = 0
or
4x + 3 = 0, and
x - 1 = 0