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Magazine Problem 7
Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. $$ \log _{\sqrt{2}}\left(4 x^{3}\right) $$
Problem 7
In Exercises \(1-33,\) solve the equation analytically. $$ 3^{7 x}=81^{4-2 x} $$
Problem 7
Solve the equation analytically. $$ \ln \left(x^{2}-99\right)=0 $$
Problem 7
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. \(e^{0}=1\)
Problem 8
How much money needs to be invested now to obtain \(\$ 2000\) in 3 years if the interest rate in a savings account is \(0.25 \%\), compounded continuously? Round your answer to the nearest cent.
Problem 8
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. \(\log _{5}(25)=2\)
Problem 8
In Exercises \(1-33,\) solve the equation analytically. $$ 9 \cdot 3^{7 x}=\left(\frac{1}{9}\right)^{2 x} $$
Problem 8
Solve the equation analytically. $$ \log \left(x^{2}-3 x\right)=1 $$
Problem 8
Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. $$ \log _{\frac{1}{3}}\left(9 x\left(y^{3}-8\right)\right) $$
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. \(\log _{25}(5)=\frac{1}{2}\)
