SOLUTION: Please help me solve this: Express the following as a single logarithm. 2log(a)1/2 + 3log(a)4 - log(a)4/5

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Question 770252: Please help me solve this: Express the following as a single logarithm.
2log(a)1/2 + 3log(a)4 - log(a)4/5
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
2log(a)1/2 + 3log(a)4 - log(a)4/5
Remember that
log x + log y = log (x*y)
log x - log y = log (x/y)
n * log x = log (x^n)
Take each part of the given expression and simplify. 
2*log(a)(1/2) = log(a)((1/2)^2) = log(a)(1/4)
3*log(a)(4) = log(a)(4^3) = log(a)(64)
So 2log(a)1/2 + 3log(a)4 = log(a)(1/4) + log(a)(64) = log(a) ((1/4)*64))
= log(a)(16)
So the expression is
log (a)(16) - log(a)(4/5)
= log(a)(16/(4/5)) = log(a)(16*5/4) = log(a)(20)
Single logarithm is log(a)(20) i.e. log 20 to the base a.
:)