Math  /  Algebra

QuestionSolve 3x5=2(5)x43^{x-5}=2(5)^{\frac{x}{4}}. The solution, to the nearest tenth, is

Studdy Solution
Calculate the value of x x using a calculator:
xln(2)+5ln(3)ln(3)14ln(5) x \approx \frac{\ln(2) + 5 \ln(3)}{\ln(3) - \frac{1}{4} \ln(5)}
x0.6931+5×1.09861.098614×1.6094 x \approx \frac{0.6931 + 5 \times 1.0986}{1.0986 - \frac{1}{4} \times 1.6094}
x0.6931+5.4931.09860.40235 x \approx \frac{0.6931 + 5.493}{1.0986 - 0.40235}
x6.18610.69625 x \approx \frac{6.1861}{0.69625}
x8.9 x \approx 8.9
The solution, to the nearest tenth, is:
8.9 \boxed{8.9}

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