Use the properties of logarithms to expand the following logarithms completely.
log(5) ^3»(xz)

Question

Use the properties of logarithms to expand the following logarithms completely.
log(5)  ^3»(xz)

anonymous · Answer

The little arrows are a radical.

psymon · Answer

The 5 is just raised to the 3rd and not a base, correct?

anonymous · Answer

The five is the base.

anonymous · Answer

The three is a cube root of xz

jdoe0001 · Answer

$\large log_5\sqrt{3xz} \ \ \ ?$

psymon · Answer

Gotcha. And I'm still not used to how people write out equations like jdoe just did, so that will always look funky xD

jdoe0001 · Answer

$\bf \huge log_5(\sqrt[3]{xz}) $ then

anonymous · Answer

Yes.

jdoe0001 · Answer

don't forget the \(    hehe

anonymous · Answer

Okay XD
But anyways. Now that we have the problem written out so it makes sense, help me solve it?? XD

jdoe0001 · Answer

keep in mind that $\bf \huge a^{\frac{n}{m}} = \sqrt[m]{a^n}$

jdoe0001 · Answer

from there just apply the log rule for the exponents

anonymous · Answer

so it's x (z/3)????

anonymous · Answer

$$\log_{5}\sqrt[3]{xz} = \log_{5}(xz)^{1/3} = \frac{1}{3}\log_5(xz)=\frac{1}{3}(\log_5x+\log_5z)$$

jdoe0001 · Answer

as shown by @walac  ^

jdoe0001 · Answer

the exponent comes out as coefficient, then you expand the factors inside as shown

anonymous · Answer

Ohhh, okay