Final Answer
$2\log_{5}\left(2\right)+\log_{5}\left(3\right)$
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Step-by-step Solution
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1
Decompose $12$ in it's prime factors
$\log_{5}\left(2^{2}\cdot 3\right)$
Learn how to solve expanding logarithms problems step by step online.
$\log_{5}\left(2^{2}\cdot 3\right)$
Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log5(12). Decompose 12 in it's prime factors. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=2^{2} and N=3. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).
Final Answer
$2\log_{5}\left(2\right)+\log_{5}\left(3\right)$
Exact Numeric Answer
$1.544$