Question

exponential and logarithmic equations question 9, 4.4.23 part 1 of 2 hw score: 29.63%, 8 of 27 points points: 0 of 1 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}=3.21\\) the solution set expressed in terms of logarithms is (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.)

Explanation:

Step1: Apply common log to both sides

$\log(10^x) = \log(3.21)$

Step2: Use log power rule simplify left side

$x\log(10) = \log(3.21)$

Step3: Use $\log(10)=1$ solve for $x$

$x = \log(3.21)$

Step4: Calculate decimal approximation

$x \approx 0.5065$

Answer:

Solution in logarithms: $\log(3.21)$
Decimal approximation: $0.507$ (rounded to three decimal places)