Question

If $3^x=5^y=7^z=105$, then $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ is equal to?

• A. $1$
• B. $0$
• C. $-1$
• D. None

Answer 1

The correct option is A $1$

$x=\frac{\log 105}{\log 3},y=\frac{\log 105}{\log 5},z=\frac{\log 105}{\log 7}$

$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{\log 3+\log 5+\log 7}{\log 105}=\frac{\log 105}{\log 105}=1$