M L Aggarwal Solutions for Exercise 4: Chapter Test

Find the value of ${\log }_{\sqrt{3}}3\sqrt{3}-{\log }_4\left(0.4\right)$

Solve the following equation for $x$:

${\log }_{\mathrm{x}}\frac{1}{243}=10$

Solve the following equation for $x$:

${\log }_{4}32=x-4$

Solve the following equation for $x$:

${\log }_7\left(2x^2-1\right)=2$

Solve the following equation for $x$:

$\log \left(x^2-21\right)=2$

Solve the following equation for $x$:

${\log }_6(x-2)+{\log }_6(x+3)=1$

Solve the following equation for $x$:

$\log (\mathrm{x}+1)+\log (\mathrm{x}-1)=\log 11+2 \log 3$

If $a=1+{\log }_{x}yz, b=1+{\log }_{y}zx \text{and} c=1+{\log }_{z}xy$, then show that $ab+bc+ca=abc$.