anonymous one year ago how do you do log(8^8 * 5^5)

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1. anonymous

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

2. anonymous

so it would be log(40^13)?

3. anonymous

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

4. anonymous

wait so how do i do it?

5. anonymous

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 :)

6. anonymous

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 $\log(a^b)=b \times \log(a)$

7. anonymous

Can you figure it out from here?

8. anonymous

wait it says to expand the problem completely

9. anonymous

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