Question

Find the Value of log2020 101 + log2020 20.​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{log_{\,2020}\,101+log_{\,2020}\,20}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}$

$\mathsf{log_{\,2020}\,101+log_{\,2020}\,20}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Product rule of logarithm:}}$

$\mathsf{log_a\,(MN)=log_a\,M+log_a\,N}$

$\mathsf{Consider,}$

$\mathsf{log_{\,2020}\,101+log_{\,2020}\,20}$

$\textsf{Using product rule,}$

$\mathsf{=log_{\,2020}\,(101{\times}20)}$

$\mathsf{=log_{\,2020}\,2020}$

$\mathsf{=1}\;\;\;\mathsf{(\because\;log_aa=1)}$

$\implies\boxed{\mathsf{log_{\,2020}\,101+log_{\,2020}\,20=1}}$

$\underline{\textbf{Find more:}}$

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