Problem preview

F-LE.4 Warmup M3-029-A10-V03

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

Separate real existence from contextual validity

Problem

Analyze \(3e^x~=~0\). Reduce the equation, determine whether a real solution exists using exponential range, and state the contextual validity.

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Analysis: 3eˣ = 0 requires eˣ = 0, which is impossible because eˣ is always positive. There is no real or contextual solution.

Analysis: 3eˣ = 0 requires eˣ = 0, which is impossible because eˣ is always positive. x = 0 is a real and contextual solution.

Analysis: 3eˣ = 0 requires eˣ = 0, so x = 0 is a real solution. There is no real or contextual solution.

Analysis: 3eˣ = 1 requires eˣ = 0, which is impossible because eˣ is always positive. There is no real or contextual solution.

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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: Separate real existence from contextual validity