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 \\(\dots\\) (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) get the answer

Explanation:

Step1: Take common log of both sides

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

Step2: Apply log power rule

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

Step3: Simplify $\log(10)=1$

$x = \log(4.23)$

Step4: Calculate decimal approximation

$x \approx 0.6263$

Answer:

In terms of logarithms: $\log(4.23)$
Decimal approximation: $0.6263$