Solve 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.

Question

10 Superscript x Baseline equals 4.68
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Part 1
The solution set expressed in terms of logarithms is StartSet log left parenthesis 4.68 right parenthesis EndSet .
  
​(Use a comma to separate answers as needed. Simplify your answer. Use integers or decimals for any numbers in the expression. Use ln for natural logarithm and log for common​ logarithm.)
Part 2
Now use a calculator to obtain a decimal approximation for the solution.
The solution set is StartSet nothing EndSet .
  

​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

Answer 1

To solve the exponential equation \( 10^x = 4.68 \), we take the common logarithm (base 10) of both sides:

\[ \log(10^x) = \log(4.68) \]

Using the logarithmic identity \( \log(a^b) = b \cdot \log(a) \), we get:

\[ x \cdot \log(10) = \log(4.68) \]

Since \( \log(10) = 1 \):

\[ x = \log(4.68) \]

Part 1: The solution set expressed in terms of logarithms is:

\[ { \log(4.68) } \]

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Part 2: Now use a calculator to obtain a decimal approximation for the solution.

Using a calculator, we find:

\[ \log(4.68) \approx 0.6701 \]

Rounding to two decimal places, we have:

\[ { 0.67 } \]

So the final answers are:

• Part 1: \( { \log(4.68) } \)
• Part 2: \( { 0.67 } \)