MTH 118 001 Precalculus S2018 Homework: 5.6 Logarithmic and Exponential Equation

Question

MTH 118 001 Precalculus S2018 Homework: 5.6 Logarithmic and Exponential Equations Score: 0 of 1 pt 5 of 14 (10 15.6.91 Solve the following equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. [Hint Mulitiply each side 9 leos What is the exact solution? Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The solution set is es (Simplity your answer. "ype an exact answer. Use integers or fractions for any numbers in the expression. Use a comma to separate ans B. There is no solution.

Explanation / Answer

( e^x - e^-x ) / 2 = 9

multiplying both sides by 2

( e^x - e^-x ) = 18

e^x - 1/ e^x = 18

let e^x = y

y - 1/y = 18

y^2 - 18y -1 = 0

y = ( 9 + sqrt 82) , (9 - sqrt 82 )

e^x = ( 9 + sqrt 82) , (9 - sqrt 82 )

taking natural log on both sides

x = ln ( 9 + sqrt 82 )

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