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Chapter 3: Problem 23
Suppose a bank account paying \(4 \%\) interest per year, compounded 12 times per year, contains \(\$ 10,555\) at the end of 10 years. What was the initial amount deposited in the bank account?
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Show that \(\sqrt{2-\sqrt{3}}=\sqrt{\frac{3}{2}}-\sqrt{\frac{1}{2}}\).
Find all numbers \(x\) that satisfy the given equation. $$ \log _{7}(x+5)-\log _{7}(x-1)=2 $$
Suppose \(x\) is a positive number and \(m, n,\) and \(p\) are positive integers. Using only the definitions of roots and integer powers, explain why $$ \left(x^{1 / m}\right)^{n}=\left(x^{1 /(m p)}\right)^{n p}. $$
Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{4} \frac{u^{2}}{v^{3}} $$
Suppose a radio is playing loudly at a sound level of 80 decibels. What decibel level would make the radio sound one-fourth as loud?
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