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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
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$\frac{1}{2}\log_{5}\left(45\right)$
Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log5(45^0.5). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Decompose 45 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=3^{2} and N=5. Evaluating the logarithm of base 5 of 5.