Question

If 8x = 43 x 23, what is the value of x? (A) 2 (B) 3 (C) 5 (D) 7 (E) 8 if the x between the two constants is raised slightly, and somehow logs are involved in this question, what the hell is this asking? I know the answer is 3, but I am lost on what the question is even about.

Answer 1

The equation is (8^x) = (4^3) * (2^3).


The x between 4^3 and 2^3 is not the variable, it is product sign.


You can use logarithm, if you prefer, but you can avoid it in this way:

8 = 2^3 => 8^x = [(2^3)]^x = 2^(3x)


And (4^3)*(2^3) = [(2^2)^3] [2^3] = (2^6)(2^3) = 2^9


Then, 2^(3x) = 2^9, and by simple inspection:

3x = 9 => x = 9/3 = 3.


And so, the answer is the option B: 3.