In this case, the base on the left is 8 and the base on the right is 16. They’re
both powers of 2, so you can express both sides as powers of 2:
Now that both sides have the same base, you can simply set the exponent
expressions equal and solve for x:
The answer is (D).
Alternative method: This is a good place to Backsolve. Try plugging the
answer choices back into the problem until you find the one that works. In
this case, work with the easier, whole numbers. If you start with (C) and x = 2,
you get 8 x = 8^2 = 64 on the left side of the equation and 16 x–1 = 16^1 = 16 on the
right side. It’s not clear whether (C) was too small or too large, so you should
probably try (D) next—it’s easier to work with than (B), which is a fraction. If x
= 4, then 8 x = 8^4 = 4,096 on the left, and 16 x–1 = 16^3 = 4,096. No need to do any
more. (D) works, so it’s the answer.