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Chapter 3: Problem 23
Use a calculator to evaluate \(f(x)=\log x\) at the indicated value of \(x .\) Round your result to three decimal places. $$x=12.5$$
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Write the logarithmic equation in exponential form. $$\ln 7=1.945 \ldots$$
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log 8 x-\log (1+\sqrt{x})=2$$
Use the acidity model given by \(\mathbf{p H}=-\log \left[\mathbf{H}^{+}\right],\) where acidity \((\mathbf{p H})\) is a measure of the hydrogen ion concentration \(\left[\mathbf{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. Apple juice has a pH of 2.9 and drinking water has a pH of \(8.0 .\) The hydrogen ion concentration of the apple juice is how many times the concentration of drinking water?
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log (3 x+4)=\log (x-10)$$
In Exercises \(103-106,\) use the change-of-base formula to rewrite the logarithm as a ratio of logarithms. Then use a graphing utility to graph the ratio. $$f(x)=\log _{1 / 4} x$$
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