Solve the exponential equation e4x - 3e2x - 18 = 0. Express the solution set in terms of natural logarithms or common logarithms.Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.
Solve the exponential equation e4x - 3e2x - 18 = 0. Express the solution set in terms of natural logarithms or common logarithms.Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CT: Chapter Test
Problem 7CT
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Question
Solve the exponential equation e4x - 3e2x - 18 = 0. Express the solution set in terms of natural logarithms or common logarithms.Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.
Expert Solution
Step 1
Given the exponential equation
Consider and put in above equation
Therefore, the equation is given by
Solve the above equation by grouping method,
Set each factor equal to zero and solve.
We know that
Therefore, and
Take the natural logarithm on both sides, we get
Recall the property
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