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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

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  1. Shi
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    Start by applying the third property to all applicable logs, so \[2\log_{3} y = \log_{3} y ^{2}\]

  4. Shi
    • 2 years ago
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    ah let me check

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

  6. gfields444
    • 2 years ago
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    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
    • 2 years ago
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    cool glad you got it :)

  8. gfields444
    • 2 years ago
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    thank you!

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