Question

If $\frac{{\log }_{a}x}{{\log }_{ab}x}=1+k+{\log }_{a}b,then$ $k=$

• A. 0
• B. 1
• C. -2
• D. -3

Answer 1

Answer: (A)

0

We know that ${\log }_{a}N=\frac{\log N}{\log a}$

$\frac{{\log }_{a}x}{{\log }_{ab}x}=\frac{\log x}{\log a}\times \frac{\log ab}{\log x}=\frac{\log a+\log b}{\log a}=1+\frac{\log b}{\log a}=1+{\log }_{a}b$

Also,

$1+{\log }_{a}b=1+k+{\log }_{a}b\Rightarrow k=0$