Question 1

Simplify LogX(logx)²

Question 2

Answer:

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

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,

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

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