Solve each equation.
$48=6e^{4k}$

Graph the given function.

$g\left(x\right)=e^{x+3}-1$

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\text{hr}$, which means its population is governed by the function $p\left(t\right)=150\cdot{2^{\frac{t}{12}}}$, where $t$ is the number of hours after the first observation.

What is the population $4~\text{days}$ after the first observation?

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\text{hr}$, which means its population is governed by the function $p\left(t\right)=150\cdot{2^{\frac{t}{12}}}$, where $t$ is the number of hours after the first observation.

How long does it take the population to triple in size?

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\text{hr}$, which means its population is governed by the function $p\left(t\right)=150\cdot{2^{\frac{t}{12}}}$, where $t$ is the number of hours after the first observation.

How long does it take the population to reach $10,000$?

Solve each equation.

$7^{y-3}=50$

Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.

${\log }_{6}60$

Changing bases Convert the following expressions to the indicated base.

$\ln \mid x\mid$ using base 5

Convert the following expressions to the indicated base.

$a^{\frac{1}{\ln a}}$ using basa e, for $a>0$ and $a\ne 1$