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Decompose $100$ in it's prime factors
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$\log_{5}\left(10^{2}\right)$
Learn how to solve differential calculus problems step by step online. Expand the logarithmic expression log5(100). Decompose 100 in it's prime factors. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Decompose 10 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 and N=5.