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Magazine Problem 8
In Problems \(7-12\), rewrite the given logarithmic expression as an equivalent exponential expression. $$ \log _{5} \frac{1}{25}=-2 $$
Problem 9
In Problems \(7-12\), rewrite the given logarithmic expression as an equivalent exponential expression. $$ \log _{\sqrt{3}} 81=8 $$
Problem 9
Solve the given exponential equation. $$ 2^{x}=8^{2 x-3} $$
Problem 9
Sketch the graph of the given function \(f\). Find the \(y\) -intercept and the horizontal asymptote of the graph. State whether the function is increasing or decreasing. $$ f(x)=3-\left(\frac{1}{5}\right)^{x} $$
Problem 9
Initially 200 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by \(3 \%\). Construct an exponential model \(A(t)=A_{0} e^{k t}\) for the amount remaining of the decaying substance after \(t\) hours. Find the amount remaining after 24 hours.
Problem 10
In Problems \(7-12\), rewrite the given logarithmic expression as an equivalent exponential expression. $$ \log _{16} 2=\frac{1}{4} $$
Problem 10
Solve the given exponential equation. $$ \frac{1}{4}\left(10^{-2 x}\right)=25\left(10^{x}\right) $$
Problem 10
Sketch the graph of the given function \(f\). Find the \(y\) -intercept and the horizontal asymptote of the graph. State whether the function is increasing or decreasing. $$ f(x)=9-e^{x} $$
Problem 11
Solve the given exponential equation. $$ 5-10^{2 x}=0 $$
Problem 11
Sketch the graph of the given function \(f\). Find the \(y\) -intercept and the horizontal asymptote of the graph. State whether the function is increasing or decreasing. $$ f(x)=-1+e^{x-3} $$
