Solving exponential equations with logarithms Practice

Solving exponential equations with logarithms (ACT). Game on.

Solving exponential equations with logarithms (ACT) is a grade 11 math skill aligned to Common Core standard HSF.LE.A.4. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 solving exponential equations with logarithms (act) problems our math games drill.

CCSS HSF.LE.A.410 questions in the bank

8 plays. No signup.

Warm-upmedium

If $2e^{x}=14$ , then $x=$

Divide both sides by $2$ to get $e^{x}=7$ . Taking $\ln$ of both sides gives $x=\ln 7\textsf{.}$

Mid-gamemedium

The real number $x$ that satisfies $e^{x+3}=8$ is

Take $\ln$ of both sides: $x+3=\ln 8$ . Subtract $3$ to get $x=\ln 8-3\textsf{.}$

Mid-gamemedium

Which of the following is the real solution of $4^{x}=20$ ?

Take $\log$ of both sides: $x\log 4=\log 20$ . Divide by $\log 4$ to get $x=\dfrac{\log 20}{\log 4}\textsf{.}$

Mid-gamemedium

Solve $e^{-x}=6$ for the real value of $x$ .

Take $\ln$ of both sides: $-x=\ln 6$ . Since $-x=(-1)x$ , divide both sides by $-1$ to get $x=-\ln 6\textsf{.}$

Mid-gamemedium

If $3^{x}=18$ , then $x=$

Take $\log$ of both sides: $x\log 3=\log 18$ . Divide by $\log 3$ to get $x=\dfrac{\log 18}{\log 3}\textsf{.}$

Mid-gamemedium

The real solution of $2e^{3x}=10$ is

Divide by $2$ to get $e^{3x}=5$ . Take $\ln$ : $3x=\ln 5$ . Divide by $3$ to get $x=\dfrac{\ln 5}{3}\textsf{.}$

Mid-gamemedium

Which value of $x$ satisfies $e^{x/2}=9$ ?

Take $\ln$ of both sides: $\dfrac{x}{2}=\ln 9$ . Multiply both sides by $2$ to get $x=2\ln 9\textsf{.}$

Buzzer beatermedium

Solve for $x$ in $7e^{x}=28$ .

Divide both sides by $7$ to get $e^{x}=4$ . Taking $\ln$ of both sides gives $x=\ln 4\textsf{.}$

8 plays. No signup.

Drill it inside a game.