how do you do log(8^8 * 5^5)

Question

brunsonni · Answer

When multiplying exponents you multiply the constants and add the exponents so that would be 40^13

anonymous · Answer

so it would be log(40^13)?

anonymous · Answer

@brunsonni You may want to check that with a calculator... That's not quite accurate

anonymous · Answer

wait so how do i do it?

anonymous · Answer

You are right that if the base was the same, you could add the exponents
Ex: 2^4*2^2=2*2*2*2*2*2=2^6
But you can't just combine everything with different bases and powers :)

anonymous · Answer

As for this problem, the easiest way is to use a calculator. The mathier way is to use the properties of logarithms.

In this case, you have to know that 
$$\log_{}(a*b )=\log(a)+\log(b)$$
and that
$$\log(a^b)=b \times \log(a)$$

anonymous · Answer

Can you figure it out from here?

anonymous · Answer

wait it says to expand the problem completely

anonymous · Answer

right, so you can use the properties I listed above to expand it. You'll have to use both and I recommend using them in the order I listed