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.

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. 

 

32.6                 0.61
+3.54            x 0.45
         
36.14               305
                    + 2440