Question

The value of  log9 81 - log4 32 is​

Answer 1

$\textbf{Concept used:}$

$\textbf{Product rule:}$

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

$\textbf{Power rule:}$

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

$\textbf{Given:}$

$\log_981-\log_432$

$\text{This can be written as}$

$=\log_99^2-\log_4(16{\times}2)$

$\text{Using power and product rule, we get}$

$=2\log_99-[\log_416+\log_42]$

$=2(1)-[\log_44^2+\log_4\sqrt{4}]$

$=2-[2\log_44+\log_44^{\frac{1}{2}}]$

$=2-[2(1)+\frac{1}{2}\log_44]$

$=2-[2+\frac{1}{2}(1)]$

$=2-[2+\frac{1}{2}]$

$=2-2-\frac{1}{2}$

$=-\frac{1}{2}$

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