Question

# This is precalculus, please do not answer if you do not understand If 8^x=27, then what is 4^(2x-3)?

Answer

2^(-6 + 4 log 27 / log 64)

- Q:What is the logarithm of 8 with base 2? A:The logarithm of 8 with base 2 is 3, since 2^3 = 8.
- Q:What is x? A:We know that 8^x=27. Taking logarithm of both sides, we get x log 8 = log 27. Therefore x = log 27 / log 8.
- Q:What is 2x-3? A:2x-3 = 2(log 27 / log 8) - 3 = (log 27 / log 64) - 3.
- Q:What is 4^(2x-3)? A:4^(2x-3) = (2^2)^(2x-3) = 2^(4x-6) = 2^(-6 + 4 log 27 / log 64).