91Ó°ÊÓ

In Exercises 25-66, solve the exponential equation algebraically. Approximate the result to three decimal places. $$ e^{x^{2}-3}=e^{x-2} $$

In Exercises 27-32, evaluate the function at the indicated value of \(x\). Round your result to three decimal places. $$\text{Function} \quad \text{value}$$ $$ h(x)=e^{-x} \quad x=\frac{3}{4} $$

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) \(\log _{4} 16^{1.2}\)

In Exercises 27-30, use the properties of logarithms to simplify the expression. \(\log _{3} 3^{4}\)

In Exercises 27-32, evaluate the function at the indicated value of \(x\). Round your result to three decimal places. $$\text{Function} \quad \text{value}$$ $$ f(x)=e^{x} \quad x=3.2 $$

Radioactive Decay In Exercises 25-30, complete the table for the radioactive isotope. \(\begin{array}{cccc} & \text { Half-life } & \text { Initial } & \text { Amount After } \\ \text { Isotope } & \text { (years) } & \text { Quantity } & 1000 \text { Years }\end{array}\) $$ \begin{array}{llll} { }^{14} \mathrm{C} & 5715 & 3 \mathrm{~g} & \\ \end{array} $$

\(\log _{1.5} 1\)

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) \(\log _{3} 81^{-0.2}\)

In Exercises 25-66, solve the exponential equation algebraically. Approximate the result to three decimal places. $$ e^{-x^{2}}=e^{x^{2}-2 x} $$

In Exercises 25-66, solve the exponential equation algebraically. Approximate the result to three decimal places. $$ 4\left(3^{x}\right)=20 $$