simplify log √ 27 + log 64 log √ 1000/ log 480

asked by guest
on Nov 22, 2024 at 8:37 pm



You asked:

Simplify the expression: \(\log\left( \sqrt{27} \right) + \frac{\log\left( 64 \right) \cdot \log\left( \sqrt{1000} \right)}{\log\left( 480 \right)}\)

MathBot Answer:

Simplified:

\[ \log\left( \sqrt{27} \right) + \frac{\log\left( 64 \right) \cdot \log\left( \sqrt{1000} \right)}{\log\left( 480 \right)} = \log{\left(3 \sqrt{3} \right)} + \frac{\log{\left(64 \right)} \log{\left(10 \sqrt{10} \right)}}{\log{\left(480 \right)}} \]

Factored:

\[ \log\left( \sqrt{27} \right) + \frac{\log\left( 64 \right) \cdot \log\left( \sqrt{1000} \right)}{\log\left( 480 \right)} = \frac{3 \left(\log{\left(3 \right)} \log{\left(480 \right)} + 6 \log{\left(2 \right)} \log{\left(10 \right)}\right)}{2 \log{\left(480 \right)}} \]


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