Question

Simplify log(10^3*x^7)

Answer 1

start by using the log law for multiplication...

\[\log_{a}(ac) = \log_{a}(b) + \log_{a}(c)\]

next you need to log law for powers

\[\log_{a}(b^c) = c \times \log_{a}(b)\]

then if you are using base 10 logs

use the law

\[\log_{10}(10^a) = a \times \log_{10}(10) = a\]

hope this helps

Answer 2

So, is it 3x^7?

Answer 3

not quite

its

3 + 7log(x)

Answer 4

Do you think you could walk me through it again? Im still not really understanding it

Answer 5

ok... multiplication law

\[\log(10^3) + \log(x^7)\]

power law

\[3 \log(10) + 7 \log(x)\]

lastly same base

\[3 + 7 \log(x)\]

Answer 6

Oh dude, thank you. I got it now. You're awesome.