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Chapter 4: Problem 39
Evaluate each expression without using a calculator. $$\log _{5} 5^{7}$$
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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. $$2^{x+1}=8$$
Find the domain of each logarithmic function. $$f(x)=\log \left(\frac{x-2}{x+5}\right)$$
Explain how to solve an exponential equation when both sides cannot be written as a power of the same base. Use \(3^{x}=140\) in your explanation.
The percentage of adult height attained by a girl who is \(x\) years old can be modeled by $$f(x)=62+35 \log (x-4)$$ where \(x\) represents the girl's age (from 5 to 15 ) and \(f(x)\) represents the percentage of her adult height. Round answers to the nearest tenth of a percent. Approximately what percentage of her adult height has a girl attained at age \(13 ?\)
The logistic growth function $$ P(x)=\frac{90}{1+271 e^{-0.122 x}} $$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. Use the function to solve Exercises \(43-46\) At what age is the percentage of some coronary heart disease \(70 \% ?\)
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