Question

If ${\log }_{k}x.{\log }_{5}k={\log }_{k}5,k\ne 1,k>0$, then $x$ is equal to

• A. $k$
• B. $\frac{1}{5}$
• C. $5$
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A $k$
C $5$

$lo{g}_{y}x=\frac{lo{g}_{c}x}{lo{g}_{c}y}$

Given $lo{g}_{k}x.lo{g}_{5}k=lo{g}_{k}5$

$\frac{logx}{logk}\frac{logk}{log5}=\frac{log5}{logx}$

$(logx{)}^2=(log5{)}^2$

$logx=log5$

$x=5$