Question

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. \\(10^{x} = 4.23\\) the solution set expressed in terms of logarithms is \\(\\{\log 4.23\\}\\) (use \\(\ln\\) for natural logarithm and \\(\log\\) for common logarithm. use integers or decimals for any numbers in the expression. simplify your answer. use a comma to separate answers as needed.) now use a calculator to obtain a decimal approximation for the solution. the solution set is \\(\\{\\}\\) (use a comma to separate answers as needed. round to two decimal places as needed.)

Explanation:

Step1: Apply common log to both sides

$\log(10^x) = \log(4.23)$

Step2: Simplify left side (log rule)

$x = \log(4.23)$

Step3: Calculate decimal approximation

$x \approx 0.63$

Answer:

In terms of logarithms: $\{\log 4.23\}$
Decimal approximation: $\{0.63\}$