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Chapter 3: Problem 88
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log 3 z=2$$
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You are investing \(P\) dollars at an annual interest rate of \(r,\) compounded continuously, for \(t\) years. Which of the following would result in the highest value of the investment? Explain your reasoning. (a) Double the amount you invest. (b) Double your interest rate. (c) Double the number of years.
Solve the equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. $$\frac{1-\ln x}{x^{2}}=0$$
Use the Richter scale \(R=\log \frac{l}{I_{0}}\) for measuring the magnitudes of earthquakes. Find the magnitude \(R\) of each earthquake of intensity \(I\) (let \(I_{0}=1\) ). (a) \(I=199,500,000\) (b) \(I=48,275,000\) (c) \(I=17,000\)
Write two or three sentences stating the general guidelines that you follow when solving (a) exponential equations and (b) logarithmic equations.
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x+\ln (x-2)=1$$
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