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Magazine Problem 9
In Exercises \(1-33,\) solve the equation analytically. $$ 3^{2 x}=5 $$
Problem 9
Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. $$ \log \left(1000 x^{3} y^{5}\right) $$
Problem 9
Use the property: \(b^{a}=c\) if and only if \(\log _{b}(c)=a\) from Theorem 6.2 to rewrite the given equation in the other form. That is, rewrite the exponential equations as logarithmic equations and rewrite the logarithmic equations as exponential equations. \(\log _{25}(5)=\frac{1}{2}\)
Problem 9
How much money needs to be invested now to obtain $$\$ 5000$$ in 10 years if the interest rate in a CD is \(2.25 \%\), compounded monthly? Round your answer to the nearest cent.
Problem 10
Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. $$ \log _{3}\left(\frac{x^{2}}{81 y^{4}}\right) $$
Problem 10
In Exercises \(1-33,\) solve the equation analytically. $$ 5^{-x}=2 $$
Problem 10
Use the property: \(b^{a}=c\) if and only if \(\log _{b}(c)=a\) from Theorem 6.2 to rewrite the given equation in the other form. That is, rewrite the exponential equations as logarithmic equations and rewrite the logarithmic equations as exponential equations. \(\log _{3}\left(\frac{1}{81}\right)=-4\)
Problem 10
Solve the equation analytically. $$ \log \left(\frac{x}{10^{-3}}\right)=4.7 $$
Problem 11
Solve the equation analytically. $$ -\log (x)=5.4 $$
Problem 11
Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. $$ \ln \left(\sqrt[4]{\frac{x y}{e z}}\right) $$
