Question

How do I expand logarithms?

Answer 1

I need to expand this: \[\log_{b}(x ^{7}y^{2})\]

Answer 2

Use logarithm properties:
\[ log(ab) = log(a) + log(b)\\
log \left(\frac{a}{b}\right) = log(a) - log(b)\\
log(a^b) = b\times log(a) \]

Answer 3

Which can be used for any base, I just didn't put them in there.

Answer 4

So, we would use product property first
\(log_b(x^7 y^2) = log_b(x^7) + log_b(y^2)\)
and then take the exponents down using power property
\(log_b(x^7)+log_b(y^2) = 7log_b(x) + 2log_b(y)\).