Question

Which of the following is the simplified version of one–half log 3 x – 2 log 3 y + 4 log 3 z?

a)log 3 square root of x over y squared times z to the fourth power

b)log 3 square root of x times y squared over z to the fourth power

c)log 3 square root of x times z to the fourth power over y squared

d)log 3 x3yz

Answer 1

Are you familiar with the properties of logarithms?

\[\log_{b} (m*n) = \log_{b} m + \log_{b}n \]
\[\log_{b}(m/n) = \log_{b}m - \log_{b}n \]
\[\log_{b}m ^{x} = x \log_{b} m \]

Answer 2

yes but I tried each of the 4 potential answers and I keep getting the wrong answer. I think it might be the last one.

Answer 3

Start by applying the third property to all applicable logs, so \[2\log_{3} y = \log_{3} y ^{2}\]

Answer 4

ah let me check

Answer 5

the answer is in the list, maybe your mistake was you got \[\log_{3}\frac{ \sqrt{x} }{ y ^{2}z ^{4} }\] ??

Answer 6

I just tried it again.... the equations you gave me helped!! I see what I did wrong, of course it was simple miscalculation :p

Answer 7

cool glad you got it :)

Answer 8

thank you!