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Chapter 4: Problem 32
Evaluate each expression without using a calculator. $$\log _{3} \frac{1}{\sqrt{3}}$$
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The figure shows the graph of \(f(x)=\ln x\). Use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. (GRAPH CANNOT COPY). $$ h(x)=-\ln x $$
In Exercises \(125-128,\) determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \frac{\log _{7} 49}{\log _{7} 7}=\log _{7} 49-\log _{7} 7 $$
The loudness level of a sound, \(D,\) in decibels, is given by the formula $$D=10 \log \left(10^{12} I\right)$$ where \(I\) is the intensity of the sound, in watts per meter \(^{2}\). Decibel levels range from \(0,\) a barely audible sound, to \(160,\) a sound resulting in a ruptured eardrum. (Any exposure to sounds of 130 decibels or higher puts a person at immediate risk for hearing damage.) Use the formula to solve. The sound of a blue whale can be heard 500 miles away, reaching an intensity of \(6.3 \times 10^{6}\) watts per meter\(^{2}\). Determine the decibel level of this sound. At close range, can the sound of a blue whale rupture the human eardrum?
Write each equation in its equivalent exponential form. Then solve for \(x .\) $$ \log _{5}(x+4)=2 $$
Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set Verify this value by direct substitution into the equation. $$ 3^{x}=2 x+3 $$
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