Question

if log10^3=0.4771, then the value of log15+log2=​

Answer 1

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

$\mathsf{log\,_{10}3=0.4771}$

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

$\textsf{The value of}$

$\mathsf{log\,_{10}15+log\,_{10}2}$

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

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

$\boxed{\mathsf{log\,_a(MN)=log\,_aM+log\,_aN}}$

$\mathsf{Consider,}$

$\mathsf{log\,_{10}15+log\,_{10}2}$

$\textsf{Using product rule of logarithm, we get}$

$\mathsf{=log\,_{10}(15{\times}2)}$

$\mathsf{=log\,_{10}30}$

$\textsf{This can be written as}$

$\mathsf{=log\,_{10}(3{\times}10)}$

$\textsf{Using product rule, we get}$

$\mathsf{=log\,_{10}3+log\,_{10}10}$

$\textsf{We know that}\;\boxed{\mathsf{log\,_aa=1}}$

$\mathsf{=0.4771+1}$

$\mathsf{=1.4771}$

$\implies\boxed{\mathsf{log\,_{10}15+log\,_{10}2=1.4771}}$

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

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