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Chapter 12: Problem 41
Evaluate each expression without using a calculator. $$8^{\log _{8} 19}$$
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Solve each equation. $$\log _{2}(x-3)+\log _{2} x-\log _{2}(x+2)=2$$
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can use any positive number other than 1 in the changeof-base property, but the only practical bases are 10 and \(e\) because my calculator gives logarithms for these two bases.
a. Simplify: \(e^{\ln 3}\) b. Use your simplification from part (a) to rewrite \(3^{x}\) in terms of base \(e\)
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. $$2^{x+1}=8$$
Solve each equation in Exercises \(144-146 .\) Check each proposed solution by direct substitution or with a graphing utility. $$\ln (\ln x)=0$$
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