Problem preview

F-LE.4 Warmup M3-029-A13-V04

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 \(4(7^{2x})~=~90\), including the required isolation step and logarithm.

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Divide by 4 to isolate 7²ˣ, then take logarithms on both sides.

Divide both sides by 7 so the exponent 2x is isolated, then solve for x.

Divide by 4 to isolate 7²ˣ, then subtract 2x from both sides to remove the exponent.

Rewrite 90 as a power of 7 and then set the exponents equal.

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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