Question

Assume all given expression are defined then which of the following statement is are incorrect

• A. $log\left(y\sqrt{x}\right)=\left(logy\right)\left(\frac{1}{2}logx\right)$
• B. $2(logx+logy)=log{x}^2{y}^3-logy$
• C. $logx-logy=\frac{logx}{logy}$
• D. $4logx-3logy=log\frac{x^4}{y^{-2}}$

Answer 1

Answer: (A)

$log\left(y\sqrt{x}\right)=\left(logy\right)\left(\frac{1}{2}logx\right)$

We can see in option A ;

$\Rightarrow LHS=log\left(y\sqrt{x}\right)=logy+log\sqrt{x}=logy+\frac{1}{2}logx\ne RHS$

$\therefore$ option A is incorrect