Math  /  Algebra

Question50.3x=5975^{0.3 x}=597
The solution set expressed in terms of logarithms is {ln(597)0.3ln(5)}\left\{\frac{\ln (597)}{0.3 \ln (5)}\right\}. (Use a comma to separate answers as needed. Simplify your answer. Use integers or decimals for any numb 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
Use a calculator to find the decimal approximation of x x . First, calculate ln(597)\ln(597) and ln(5)\ln(5), then divide:
1. Calculate ln(597)\ln(597).
2. Calculate ln(5)\ln(5).
3. Divide the results:

xln(597)0.3ln(5) x \approx \frac{\ln(597)}{0.3 \ln(5)}
Using a calculator:
ln(597)6.389 \ln(597) \approx 6.389 ln(5)1.609 \ln(5) \approx 1.609 x6.3890.3×1.609 x \approx \frac{6.389}{0.3 \times 1.609} x6.3890.4827 x \approx \frac{6.389}{0.4827} x13.23 x \approx 13.23
The solution set is:
13.23 \boxed{13.23}

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