Question

Simplify LogX(logx)²​

Answer 1

`\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`