Hamilton Peterson
08/21/2024 · Senior High School
Write the expression as a single logarithm. \( 3 \log _{2} \mathrm{u}+4 \log _{2} \mathrm{v} \) \( 3 \log _{2} \mathrm{u}+4 \log _{2} \mathrm{v}=\square \) (Simplify your answer.)
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Step-by-step Solution
Calculate or simplify the expression \( 3 \log_{2} u + 4 \log_{2} v \).
Simplify the expression by following steps:
- step0: Solution:
\(3\log_{2}{\left(u\right)}+4\log_{2}{\left(v\right)}\)
- step1: Use the logarithm base change rule:
\(\log_{2}{\left(u^{3}\right)}+\log_{2}{\left(v^{4}\right)}\)
- step2: Transform the expression:
\(\log_{2}{\left(u^{3}v^{4}\right)}\)
The expression \(3 \log_{2} u + 4 \log_{2} v\) can be simplified as \(\log_{2}{(u^{3}v^{4})}\).
Quick Answer
\( 3 \log_{2} u + 4 \log_{2} v = \log_{2}{(u^{3}v^{4})} \)
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