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Chapter 3: Problem 22
Suppose a radio is playing loudly at a sound level of 80 decibels. What decibel level would make the radio sound one-fourth as loud?
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Suppose you have a calculator that can only compute square roots and can multiply. Explain how you could use this calculator to compute \(7^{3 / 4}\).
Show that if \(f\) is a function with exponential growth, then so is the square root of \(f\). More precisely, show that if \(f\) is a function with exponential growth, then so is the function \(g\) defined by \(g(x)=\sqrt{f(x)}\)
Show that if \(x\) and \(y\) are positive numbers with \(x \neq y,\) then $$ \frac{x-y}{\sqrt{x}-\sqrt{y}}=\sqrt{x}+\sqrt{y}. $$
The most intense recorded earthquake in Wyoming occurred in \(1959 ;\) it had Richter magnitude \(6.5 .\) The most intense recorded earthquake in Illinois occurred in 1968 ; it had Richter magnitude 5.3. Approximately how many times more intense was the 1959 earthquake in Wyoming than the 1968 earthquake in Illinois?
Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{4}\left(u^{3} v^{4}\right) $$
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