91Ó°ÊÓ

Solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate \(x\) to 3 decimal places. \(e^{5 x}=17\) using the natural log

Solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate \(x\) to 3 decimal places. \(3(1.04)^{3 t}=8\) using the common log

Solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate \(x\) to 3 decimal places. \(3^{4 x-5}=38\) using the common log

Solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate \(x\) to 3 decimal places. \(50 e^{-0.12 t}=10\) using the natural log

Use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth. \(7 e^{3 x-5}+7.9=47\)

Use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth. \(\ln (3)+\ln (4.4 x+6.8)=2\)

Atmospheric pressure \(P\) in pounds per square inch is represented by the formula \(P=14.7 e^{-0.21 x}\) , where \(x\) is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.369 pounds per square inch? (Hint: there are 5280 feet in a mile)

The magnitude \(M\) of an earthquake is represented by the equation \(M=\frac{2}{3} \log \left(\frac{E}{E_{0}}\right)\) where \(E\) is the amount of energy released by the earthquake in joules and \(E_{0}=10^{4.4}\) is the assigned minimal measure released by an earthquake. To the nearest hundredth, what would the magnitude be of an earthquake releasing 1.4\(\cdot 10^{13}\) joules of energy?

Use the definition of a logarithm along with the one-to-one property of logarithms to prove that \(b^{\log _{b} x}=x\)

Recall the formula for continually compounding interest, \(y=A e^{k t} .\) Use the definition of a logarithm along with properties of logarithms to solve the formula for time \(t\) such that \(t\) is equal to a single logarithm.