Question

If $f\left(x\right)=\ln x;$ where $x\in R^{+},$ then

• A. $f(x+y)=f\left(x\right)+f\left(y\right)$
• B. $f(x\cdot y)=f\left(x\right)+f\left(y\right)$
• C. $f(x+y)=f\left(x\right)\cdot f\left(y\right)$
• D. $f(x\cdot y)=f\left(x\right)\cdot f\left(y\right)$

Answer 1

The correct option is B $f(x\cdot y)=f\left(x\right)+f\left(y\right)$

Given $f\left(x\right)=\ln x$
Then $f(x+y)=\ln (x+y)$

And $f(x\cdot y)=\ln (x\cdot y)$
$\Rightarrow f(x\cdot y)=\ln \left(x\right)+\ln \left(y\right)$
$\Rightarrow f(x\cdot y)=f\left(x\right)+f\left(y\right)$