gfields444 2 years ago 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

1. Shi

Are you familiar with the properties of logarithms? $\log_{b} (m*n) = \log_{b} m + \log_{b}n$ $\log_{b}(m/n) = \log_{b}m - \log_{b}n$ $\log_{b}m ^{x} = x \log_{b} m$

2. gfields444

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.

3. Shi

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

4. Shi

ah let me check

5. Shi

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

6. gfields444

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

7. Shi

cool glad you got it :)

8. gfields444

thank you!