Question

If log2 = 0.301 and log3 = 0.4771, find the value of log^72^5​

Answer 1

$\textbf{Formula used:}$

$\textbf{Product rule:}$

$\boxed{\bf\,log_a(MN)=log_aM+log_aN}$

$\textbf{Power rule:}$

$\boxed{\bf\,log_aM^n=n\;log_aM}$

$\textbf{Given:}$

$\log\,2=0.301\;\text{and}\;\log\,3=0.4771$

$\textbf{To find:}$

$\text{The value of \log\,72^5 }$

$\text{Consider,}$

$\log\,72^5$

$\text{Using power rule of logarithm}$

$=5\,\log\,72$

$=5\,\log(8{\times}9)$

$\text{Using product rule of logarithm}$

$=5(\log\,8+\log\,9)$

$=5(\log\,2^3+\log\,3^2)$

$\text{Using power rule of logarithm}$

$=5(3\,\log\,2+2\,\log\,3)$

$=5(3(0.301)+2(0.4771))$

$=5(0.903+0.9542)$

$=5(1.8572)$

$=9.286$

$\therefore\textbf{The value of \bf\log\,72^5 is 9.286}$

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