Log Question: log 4{sqrt}32y

[heather]

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]

"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]

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]

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)