04 Logarithmic Functions Online Quiz Questions

True or false: If $b>1$, then the function $y=\log_b x$ is increasing on its domain.

For which values of $x$ is $\log_3(x-4)$ defined?

Evaluate $\log_2 32$.

Select all conditions required for $\log_b x$ to be defined as a real logarithm.

Solve $2^{x+1}=16$ for $x$.

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

Select all valid logarithm identities for positive quantities and a valid base $b$.

Which expression is equivalent to $\log_7 20$ by the change-of-base formula?

Solve $\ln x+\ln(x-3)=\ln 4$.

Solve $5^x=17$ to the nearest whole number.

Solve the inequality $\log_2(x-1)\le 3$. State the solution set and explain how both the base and the logarithm's domain affect the answer.

What does the notation $\ln x$ mean?

A population follows the model $P(t)=500e^{0.04t}$, where $t$ is measured in years. After how many years will the population reach $800$? Round to two decimal places. The absolute tolerance is $0.01$ years.

What is the domain of the function $f(x)=\log_3(x-4)$?

True or false: The function $y=\log_{1/4}x$ is decreasing on its domain.

Which expression correctly represents $\log_7 20$ using natural logarithms?

What is the solution to $\ln x+\ln(x-3)=\ln 4$?

Solve the inequality $\log_2(x-1)\le3$.