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Chapter 12: Problem 74
Write each equation in its equivalent exponential form. Then solve for \(x .\) $$\log _{5}(x+4)=2$$
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Logarithmic models are well suited to phenomena in which growth is initially rapid, but then begins to level off. Describe something that is changing over time that can be modeled using a logarithmic function.
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 nuptured eardrum. Use the formula to solve Exercises. What is the decibel level of a normal conversation, \(3.2 \times 10^{-6}\) watt per meter \(^{2} ?\)
Simplify: \(\left(-2 x^{3} y^{-2}\right)^{-4}\)
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When graphing a logarithmic function, I like to show the graph of its horizontal asymptote.
Solve: $$\frac{3}{x+1}-\frac{5}{x}=\frac{19}{x^{2}+x}$$
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