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.

Question

Wagner

Mathematics

3 April, 23:05

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.

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Answers (1)

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Abdiel Pruitt · 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.