SOLUTION: how do you solve? 27^4x=9

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: how do you solve? 27^4x=9      Log On


   

Question 585345: how do you solve?
27^4x=9
Found 2 solutions by Earlsdon, nerdybill:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
27%5E%284x%29+=+9 Replace: 27+=+3%5E3 and 9+=+3%5E2
%283%5E3%29%5E%284x%29+=+3%5E2 Simplify.
3%5E%2812x%29+=+3%5E2 The bases are equal so the exponents must be equal.
12x+=+2 Divide by 12.
x+=+2%2F12 Simplify.
x+=+1%2F6

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
I'll assume you meant the exponent to be "4x".
.
27%5E%284x%29=9
log%2827%2C27%5E%284x%29%29=log%2827%2C9%29
4x=log%2827%2C9%29
4x=log%289%29%2Flog%2827%29
x=log%289%29%2F%284%2Alog%2827%29%29
x=0.1667