Expand the logarithmic expression $\log_{b}\left(\sqrt[4]{\frac{m^{16}n^{20}}{b^5c^5}}\right)$

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Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression logb(((m^16*n^20)/(b^5*c^5))^(1/4)). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=m^{16} and N=n^{20}. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=b^5 and N=c^5.