Answer:
[tex]\log \:_{10}\left(x\right)\left(\log \:_{10}\left(x\right)\right)^2=\log \:_{10}\left(x\right)^3[/tex]
Step-by-step explanation:
Considering the expression
[tex]\log _{10}\left(x\right)\left(\log _{10}\left(x\right)\right)^2[/tex]
Simplifying
[tex]\log _{10}\left(x\right)\left(\log _{10}\left(x\right)\right)^2[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]
[tex]\log _{10}\left(x\right)\left(\log _{10}\left(x\right)\right)^2=\:\log _{10}\left(x\right)^{1+2}[/tex]
[tex]=\log _{10}\left(x\right)^{1+2}[/tex]
[tex]\mathrm{Add\:the\:numbers:}\:1+2=3[/tex]
[tex]=\log _{10}\left(x\right)^3[/tex]
Therefore,
- [tex]\log \:_{10}\left(x\right)\left(\log \:_{10}\left(x\right)\right)^2=\log \:_{10}\left(x\right)^3[/tex]
