## Log Question: log 4{sqrt}32y

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
heather
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Joined: Tue Mar 16, 2010 3:59 pm
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### Log Question: log 4{sqrt}32y

The question I am stuck on is log 4{sqrt}32y
i know if there is no base shown it is log base 10, but when i plug it into my calculator I get zero for my answer.

How do i go about solving this question?

nicknation
Posts: 23
Joined: Wed Mar 11, 2009 3:28 pm

### Re: Log Question: log 4{sqrt}32y

"solving" means an equation. did you mean "simplify" or "expand" or "evaluate" or something?

is the base 10? or 4? what is inside the {sqrt}?

thnx

heather
Posts: 2
Joined: Tue Mar 16, 2010 3:59 pm
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### Re: Log Question: log 4{sqrt}32y

I'm sorry,
the base is 10, and its supposed to be the square root of 32y.
I'm sorry, I'm still getting the hang of posting math language, but I am getting there.
And the question says "express each as a sum, difference or multiple of logarithms. Wherever possible, evaluate logarithms of the result."

nicknation
Posts: 23
Joined: Wed Mar 11, 2009 3:28 pm

### Re: Log Question: log 4{sqrt}32y

so you're supposed to expand log10(4 * sqrt[32y]) ?

the sqrt[32] is sqrt[2 * 16] = 4 * sqrt[2]

the sqrt[] is the 1/2 power

to expand use the rules they show here

you can evaluate the log10(16) and the (1/2) * log10(2) but not the (1/2) * log10(y)