Solve the exponential equation. Express the solution set in terms of natural log

Question

Solve the exponential equation. Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. e^2x - 14e^x +13 = 0 What is the solution in terms of natural logarithms? The solution set is {}. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression.) What is the decimal approximation for the solution? The solution set is {}. (Use a comma to separate answers as needed. Round to two decimal places as needed.) Enter your answer in each of the answer boxes.

Explanation / Answer

e^2x --14e^x + 13 =0

Let e^x be y: y^2 -14y +13 =0

factorise : y^2 -13y -y +13 =0

y(y -13) -1(y -13) =0

(y -1)(y -13) =0

y =1 ; y = 13

a) e^x =1 ---> x = ln(1) =0

x=0

e^x = 13 ---> x= ln(13)

b) From calculator Now x = 0 , 2.56

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