MATH
posted by mathemagiacian .
Suppose 81^x = 64. What is 27^{x+1}?
Give me a clear explanation with the answer. Thanks! :)

clearly, x = log_{81}64 = 1/4 log_{3}64
27^{x+1} = 27*3^3x
= 27*3^(3(1/4 log_{3}64))
= 27*3^(3/4 log_{3}64)
= 27*3^((log_{3}64) * 3/4)
= 27*64^(3/4)
= 27*2^(9/2)
= 27*16√2
= 432√2