Problem preview

F-LE.4 Warmup M3-029-A13-V02

Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.

Solve an exponential equation by isolating the exponential factor and taking logarithms

Problem

Describe the appropriate method for solving \(3^x~=~20\) and justify why logarithms or change of base are needed.

Answer choices

Choose your path.

Preview only

Use logarithms or the change-of-base formula, because 20 is not an exact power of 3.

Divide both sides by 3 first so the exponent is isolated, then solve the simpler equation for x.

Subtract 3 from both sides to get x by itself, because the base and exponent can be separated like a linear expression.

Rewrite 20 as a nearby power of 3 and then set the exponents equal, since 3³ is close to 20.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

More than a preview

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

Curriculum context

Course: Math III
Standard: F-LE.4
Category: Functions
Domain: Linear, Quadratic, and Exponential Models
Objective: Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Problem type: Solve an exponential equation by isolating the exponential factor and taking logarithms