Question

Question one pls
algebra 2
logarithms

Answer 1

Condense the logarithm on the right side:

`3\log_b(p)-\left(2\log_b(t)+\frac12\log_b(r)\right)`

`n\log_b(m)=\log_b(m^n) \implies \log_b(p^3)-\left(\log_b(t^2)+\log_b\left(r^(\frac12)\right)\right)`

`\log_b(m)+\log(n)=\log_b(mn) \implies \log_b(p^3)-\log_b\left(t^2r^(\frac12)\right)`

`\log_b(m)-\log(n)=\log_b\left(\frac mn\right) \implies \log_b\left((p^3)/(t^2r^(\frac12))\right)`

So,

`x=(p^3)/(t^2r^(\frac12))`

and
`r^(\frac12)=√(r)`, which makes (4) the correct choice.