91Ó°ÊÓ

In Problems \(13-18\), find the exact value of the given logarithm. $$ \log _{4} 64 $$

Solve the given exponential equation. $$ \left(\frac{1}{2}\right)^{-x+2}=8\left(2^{x-1}\right)^{3} $$

The amount remaining of a radioactive substance after \(t\) hours is given by \(A(t)=100 e^{k t} .\) After 12 hours, the initial amount has decreased by \(7 \%\). How much remains after 48 hours? What is the half-life of the substance?

Solve the given exponential equation. $$ \frac{1}{3}=\left(2^{|x|-2}-1\right)^{-1} $$

In Problems \(13-18\), find the exact value of the given logarithm. $$ \log _{2}\left(2^{2}+2^{2}\right) $$

In Problems \(13-18\), find the exact value of the given logarithm. $$ \log _{9} \frac{1}{3} $$

Find an exponential function \(f(x)\) \(=b^{x}\) such that the graph of \(f\) passes through the given point. $$ (2, e) $$

Solve the given exponential equation. $$ \left(\frac{1}{3}\right)^{x}=9^{1-2 x} $$

Strontium-9o is a dangerous radioactive substance found in acid rain. As such it can make its way into the food chain by polluting the grass in a pasture on which milk cows graze. The halflife of strontium-9o is 29 years. (a) Find an exponential model (3) for the amount remaining after \(t\) years. (b) Suppose a pasture is found to contain Str-90 that is 3 times a safe level \(A_{0} .\) How long will it be before the pasture can be used again for grazing cows?

Find an exponential function \(f(x)\) \(=b^{x}\) such that the graph of \(f\) passes through the given point. $$ (-2,9) $$