91Ó°ÊÓ

Solve the exponential equation. Round to three decimal places, when needed. $$e^{x^{2}+1}-2=3$$

Sketch the graph of each function. $$g(x)=10(2)^{x}$$

Evaluate each expression without using a calculator. $$\log _{2} \sqrt{2}$$

The half-life of plutonium-238 is 88 years. (a) Given an initial amount of \(A_{0}\) grams of plutonium238 at time \(t=0,\) find an exponential decay model, \(A(t)=A_{0} e^{k t},\) that gives the amount of plutonium238 at time \(t, t \geq 0\). (b) Calculate the time required for \(A_{0}\) grams of plutonium- 238 to decay to \(\frac{1}{3} A_{0}\).

Solve the exponential equation. Round to three decimal places, when needed. $$5+e^{x^{2}+1}=8$$

Sketch the graph of each function. $$h(x)=-5(3)^{x}$$

In Exercises \(21-30,\) write each logarithm as a sum and\or difference of logarithmic expressions. Eliminate exponents and radicals and evaluate logarithms wherever possible. Assume that \(a, x, y\) \(z>0\) and \(a \neq 1\). $$\log _{a} \sqrt{\frac{z^{5}}{x y^{4}}}$$

Evaluate each expression without using a calculator. $$\log _{7} 49$$

Evaluate each expression without using a calculator. $$\log _{3} \frac{1}{81}$$

In Exercises \(21-30,\) write each logarithm as a sum and\or difference of logarithmic expressions. Eliminate exponents and radicals and evaluate logarithms wherever possible. Assume that \(a, x, y\) \(z>0\) and \(a \neq 1\). $$\log \sqrt[3]{\frac{x y^{3}}{z^{5}}}$$