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Math  /  Algebra

QuestionSolve the exponential equation. Express the solution in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. ex=19.56e^{x}=19.56
The solution set expressed in terms of logarithms is {ln⁡19.56}\{\ln 19.56\}. (Use a comma to separate answers as needed. Simplify your answer. Use integers or decimals for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is □\square (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. We are given the exponential equation ex=19.56 e^x = 19.56 .
2. The solution should be expressed in terms of natural logarithms or common logarithms.
3. We need to find a decimal approximation for the solution using a calculator.

STEP 2

1. Express the solution in terms of natural logarithms.
2. Use a calculator to find the decimal approximation.

STEP 3

To solve the equation ex=19.56 e^x = 19.56 , we take the natural logarithm of both sides. This gives:
x=ln⁡(19.56) x = \ln(19.56)

STEP 4

Now, use a calculator to find the decimal approximation of ln⁡(19.56) \ln(19.56) .
Calculate ln⁡(19.56) \ln(19.56) using a calculator:
x≈2.974 x \approx 2.974
Round to two decimal places:
The solution set is 2.97 \boxed{2.97} .

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