Question

Expand. Express in terms of sums and differences
loga^5x^5yz^6

Answer 1

I'm assuming everything is inside the log function?

Answer 2

yes

Answer 3

I'd start expanding with \[\ln (ab)=\ln a+\ln b\]

Answer 4

\[loga ^{5x5}yz ^{6}\]

Answer 5

And then I'd use \[\ln x^a = a \ln x\]

Answer 6

\[5x5\] is in the exponent?

Answer 7

yes

Answer 8

the log of a product is the sum of logs of each term in the product, so you can split that up, like i said with \[\log (ab) = \log a+\log b\]

Answer 9

and you can bring the exponent in a log function down to be a product with the log of the base, like i said with \[\log a^n = n\times \log a\]

Answer 10

Unless I've missed something, you can fully expand the given function using only those two laws of logarithms