SOLUTION: Simplify without a calculator. Show all steps 4 log base 3 of 1/3 + 2log base 27 of 9

Question 714277: Simplify without a calculator. Show all steps
4 log base 3 of 1/3 + 2log base 27 of 9
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Simplify without a calculator. Show all steps
4 log base 3 of 1/3 + 2log base 27 of 9
..
4 log base 3 of 1/3
=log3(1/3)^4
=log3(1/81)
=log3(1/3)^4)
=log3(1/3)^3)*(1/3)
=log3[(3^-3)*(3^-1)]
=log3(3^-3)+log3(3^-1)
log of base raised to a power=power
=-3-1=-4
..
2log base 27 of 9
=log27(9^2)
=log27(81)
=log27(3^3)+log27(3^1)
=log27(27)+log27(3)
=1+1/3
=4/3
..
4 log base 3 of 1/3 + 2log base 27 of 9=-4+4/3=-12/3+4/3=-8/3
RELATED QUESTIONS
Find the exact value of (log base 2 of 3)(log base 3 of 4)(log base 4 of 5)...(log base n (answered by Fombitz)

what is log base 4 of 27-2log base 4 of 3 as a single a... (answered by lwsshak3)

Express y as a function of x. What is the domain? a) log(base 2)xy = 3log(base 2)x b)... (answered by stanbon,rothauserc)

Hi! i have a test tomorrow on logs and i am having trouble knowing how to evaluate a log... (answered by ikleyn)

Find the exact value of log base of 4[log base of 3(log base of 2)8)] without using a... (answered by stanbon)

1.Write as a difference of logarithms a) log(base 4)11 b) log(base 3)12 c) log(base... (answered by MathLover1)

how do u do 4^(log(base 8) of 27 without a calculator Problem:... (answered by jim_thompson5910,Edwin McCravy)

2log[base 3](x+4)-log[base... (answered by ewatrrr,stanbon)

How would you solve log of 54 base 3 and log of 48 base 4 without a calculator? I know if (answered by stanbon,herosz)