Logarithmic Functions Online Quiz Questions

Simplify $\log_5\left(5^{3x-1}\right)$.

True or false: The domain of $f(x)=\log_2(x-3)+1$ is $x>3$.

Solve $\log_4(x)=3$. Enter the value of $x$.

Using the change-of-base formula, approximate $\log_5(37)$ to three decimal places.

True or false: For positive $M$ and $N$, and a valid logarithm base $b$ with $b>0$ and $b\ne1$, $\log_b(M+N)=\log_b(M)+\log_b(N)$.

Select all statements that are true for the parent function $y=\log_b(x)$, where $b>0$ and $b\ne1$.

What is the standard name of the property that rewrites $\log_b(MN)$ as $\log_b(M)+\log_b(N)$?

Solve $\log_{1/3}(x)\le-2$.

For the equation $\ln(x)+\ln(x-3)=\ln(10)$, select all correct statements about solving it.

Solve $2^x=7$. Show the logarithmic steps and give both an exact expression and an approximation to three decimal places.

A population follows $P(t)=500(1.08)^t$, where $t$ is measured in years. How long will it take for the population to reach 750? Round to the nearest hundredth; enter the time in years.

Condense $2\ln(x)+\ln(y)-\ln(4)$ into a single logarithm.

True or false: If $0<b<1$, then $\log_b(x)$ is decreasing, and solving a logarithmic inequality by converting to exponential form reverses the inequality direction.

For the transformed function f(x)=$\log_2(x-3)+1$, which statement correctly identifies both its domain and its vertical asymptote?

Which expression gives the correct change-of-base form for $\log_5(37)$?

Solve the equation $\log_4(x)=3$. Enter the exact value of x.

Assuming x>0 and y>0, which expression correctly expands $\log_2\left(\frac{8x^3}{y}\right)$?

What is the solution set of $\log_{1/3}(x)\le -2$?