Question

Select all that apply

Answer 1

Third option

`\log _(10)\left(20x^5\right)-1\\`

Explanation:

`5\log _(10)\left(x\right)+\log _(10)\left(20\right)-\log _(10)\left(10\right)\\\\\mathrm{Apply\:log\:rule}:\\\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)\\\\5\log _(10)\left(x\right)=\log _(10)\left(x^5\right)\\\\=\log _(10)\left(x^5\right)+\log _(10)\left(20\right)-\log _(10)\left(10\right)\\\\\mathrm{Apply\:log\:rule}:\\\quad \log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)\\\\\log _(10)\left(x^5\right)+\log _(10)\left(20\right)=\log _(10)\left(20x^5\right)\\\\`

`=\log _(10)\left(x^5\cdot \:20\right)-\log _(10)\left(10\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\\\=\log _(10)\left(20x^5\right)-1`