Question 418142
Express the function
f(x)=log_(3)(9^(6 x+4) 81^(6 x+ 8))
without logarithms.

..
f(x)=log(3*9^(6x+4)*81^(6x+8))
    change to base 3
    =log(3*(3^2)^(6x+4)*3^4^(6x+8))
    multiply exponents
    =log(3*(3)^12x+8*(3)^(24x+32))
    add exponents
    =log(3*(3^(36x+40))
    =log(3^(36x+41))
    use exponent rule for logarithms
    =(36x+41)*log3
    use calculator for log 3
    =(36x+41)*.477
ans:
f(x)=17.18x+19.56