Which of the following best describes the equation $y={\log }_b\left(x\right)$ in exponential form?

Simplify the expression ${\log }_3\left(3^{2x+1}\right)$.

Convert $4^{x-1}=\frac{1}{32}$ into logarithmic form and solve for $x$.

Compute ${\log }_{{}_{27}}\left(\sqrt{3}\right)$.

A population grows according to $P\left(t\right)=200\cdot 2^{\frac{t}{3}}$, where $t$ is in months. Solve for $t$ when $P\left(t\right)=1600$.