Question

Let ${\log }_{a}ab=x$ then find the value of ${\log }_{b}ab$.

Answer 1

Given ${\log }_{a}ab=x$

or, ${\log }_{a}a+{\log }_{a}b=x$

or, $1+{\log }_{a}b=x$

or, ${\log }_{a}b=x-1$

or, ${\log }_{b}a=\frac{1}{x-1}$

or, $1+{\log }_{b}a=\frac{x}{x-1}$

or, ${\log }_{b}b+{\log }_{b}a=\frac{x}{x-1}$

or, ${\log }_{b}ab=\frac{x}{x-1}$.