Suppose 81^x = 64. What is 27^{x+1}?

Question

Give me a clear explanation with the answer. Thanks! :)

Answer 1

clearly, x = log₈₁64 = 1/4 log₃64

27^{x+1} = 27*3^3x
= 27*3^(3(1/4 log₃64))
= 27*3^(3/4 log₃64)
= 27*3^((log₃64) * 3/4)
= 27*64^(3/4)
= 27*2^(9/2)
= 27*16√2
= 432√2