Question

If ${\log }_{105}7=a,{\log }_{7}5=b$ then ${\log }_{35}105$ is equal to

• A. ab
• B. $(b+1)a$
• C. $\frac{1}{ab}$
• D. $\frac{1}{a(b+1)}$

Answer 1

Answer: (D)

$ab={\log }_{105}7\cdot {\log }_{7}5={\log }_{105}5$
Now ${\log }_{35}105=\frac{1}{{\log }_{105}35}=\frac{1}{{\log }_{105}5+{\log }_{105}7}=\frac{1}{ab+a}=\frac{1}{a(b+1)}$