SOLUTION: Express the function f(x) = logbase3(27^(3 x + 6) 81^(6 x + 8)) without logarithms.

Algebra ->  Exponents -> SOLUTION: Express the function f(x) = logbase3(27^(3 x + 6) 81^(6 x + 8)) without logarithms.      Log On


   

Question 951682: Express the function
f(x) = logbase3(27^(3 x + 6) 81^(6 x + 8))

without logarithms.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+log%283%2C%2827%5E%283x+%2B+6%29+81%5E%286+x+%2B+8%29%29%29
f%28x%29+=+y
f%28x%29+=+log%283%2C%28%283%5E3%29%5E%283x+%2B+6%29+%283%5E4%29%5E%286x+%2B+8%29%29%29
f%28x%29+=+log%283%2C%283%5E%289x+%2B+18%29%2A3%5E%2824x+%2B+32%29%29%29
f%28x%29+=+log%283%2C%283%5E%289x+%2B+18%2B24x+%2B+32%29%29%29
y=+%28log%283%5E%2833x%2B50%29%29%29%2F%28log%283%29%29
ylog%283%29=+log%283%5E%2833x%2B50%29%29
log%283%5Ey%29=+log%283%5E%2833+x%2B50%29%29 .......since log same then
3%5Ey=3%5E%2833x%2B50%29 ......... since bases same then exponents same too
y=33x%2B50
or
f%28x%29+=33x%2B50