Solve the following exponential equation by taking the natur

Solve the following exponential equation by taking the natural logarithm on both sides. Express the solution in terms of natural logarithms. ? Then, use a calculator to obtain a decimal approximation for the solution. e^(2-9x)=1306    NATURAL LOGARITHM and DECIMAL

Solve the following exponential equation by taking the natural logarithm on both sides. Express the solution in terms of natural logarithms. Then, use a calculator to obtain a decimal approximation for the solution. 2-9-1306 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.)

Solution

e ^ ( 2-9x ) = 1306

taking natural log on both sides

(2-9x) ln e = ln 1306

ln e = 1

hence , 2-9x = ln 1306

subtracting 2 from both sides

-9x = ln 1306 - 2

dividng both sides by -9 to isolate x

x = (ln 1306-2) / -9

decimal approximation is

ln 1306 = 7.1747

plugging the value

x = (7.1747 - 2 )/ -9 = -.5749