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Chapter 4: Problem 97
Evaluate or simplify each expression without using a calculator. $$e^{\ln 5 x^{2}}$$
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Evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: \(\log _{3} 81\) b. Evaluate: \(2 \log _{3} 9\) c. What can you conclude about $$\log _{3} 81, \text { or } \log _{3} 9^{2} ?$$
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. $$3^{x+1}=9$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can solve \(4^{x}=15\) by writing the equation in logarithmic form.
In Exercises \(53-56,\) rewrite the equation in terms of base \(e\). Express the answer in terms of a natural logarithm and then round to three decimal places. $$ y=1000(7.3)^{x} $$
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 I3 0 decibels or higher puts a person at immediate risk for hearing damage.) What is the decibel level of a normal conversation, \(3.2 \times 10^{-6}\) watt per meter \(^{2} ?\)
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