Question

3. Find x, if 2log3 + 1/2log4 - log2 = logx.
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Answer 1

$\textbf{Formula used:}$

$\textbf{Product rule:}$

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

$\textbf{Qutient rule:}$

$\boxed{\bf\,log_a(\frac{M}{N})=log_aM-log_aN}$

$\textbf{Power rule:}$

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

$\textbf{Given;}$

$2\,log\,3+\frac{1}{2}log\,4-log\,2=log\,x$

$\textbf{To find: x}$

$2\,log\,3+\frac{1}{2}log\,4-log\,2=log\,x$

$\text{By using power rule, we get}$

$log\,3^2+log\,4^{\frac{1}{2}}-log\,2=log\,x$

$log\,9+log\,2-log\,2=log\,x$

$log\,9=log\,x$

$\implies\boxed{\bf\,x=9}$

$\therefore\textbf{The value of x is 9}$

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Answer 2

here is your answer.....

hope it helps.......