Question

I need help on logarithmic expansion. The equation looks like this: log[9](√9:((s^(4)t)/(81))) (it needs to be expanded) If you have trouble interpreting the equation, go to mathway.com, type it in, and press the show button.

Answer 1

do you want the answer?

Answer 2

like exact result?

Answer 3

Assuming tis is your expression:\[\log_9{\sqrt[9]{\frac{s^4t}{81}}}\]Then the first step would be to express the 9th root of the expression as a power, e.g. how would you express \(\sqrt[9]{x}\) as \(x^a\) - what would 'a' be here?

Also note that \(81=9^2\)

Then use these log rules to simplify your expression:
1. \(\log_b{x^a}=a\log_b{x}\)
2. \(\log_b{\frac{x}{y}}=\log_b{x}-\log_b{y}\)