Question

Simplify LogX(logx)²​

Answer 1

Answer:

$\log \:_{10}\left(x\right)\left(\log \:_{10}\left(x\right)\right)^2=\log \:_{10}\left(x\right)^3$

Step-by-step explanation:

Considering the expression

$\log _{10}\left(x\right)\left(\log _{10}\left(x\right)\right)^2$

Simplifying

$\log _{10}\left(x\right)\left(\log _{10}\left(x\right)\right)^2$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$\log _{10}\left(x\right)\left(\log _{10}\left(x\right)\right)^2=\:\log _{10}\left(x\right)^{1+2}$

$=\log _{10}\left(x\right)^{1+2}$

$\mathrm{Add\:the\:numbers:}\:1+2=3$

$=\log _{10}\left(x\right)^3$

Therefore,

• $\log \:_{10}\left(x\right)\left(\log \:_{10}\left(x\right)\right)^2=\log \:_{10}\left(x\right)^3$