91Ó°ÊÓ

Expanding a Logarithmic Expression In Exercises \(37-58\) , use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.) $$\ln \sqrt[4]{x^{3}\left(x^{2}+3\right)}$$

Polynomial and rational functions are examples of______________functions.

Fill in the blanks. The inverse function of the exponential function \(f(x)=a^{x}\) is called the ________ function with base \(a\)

Fill in the blanks. To solve exponential and logarithmic equations, you can use the following One- to-One and Inverse Properties. (a) \(a^{x}=a^{y}\) if and only if _____. \(\quad\) (b) \(\log _{a} x=\log _{a} y\) if and only if _____. (c) \(a^{\log _{a} x}=\) _____ \(\quad\) (d) \(\log _{a} a^{x}=\) _____

An exponential growth model has the form ________, and an exponential decay model has the form _________

Fill in the blanks. The common logarithmic function has base _______ .

Fill in the blanks. An _____ solution does not satisfy the original equation.

Exponential and logarithmic functions are examples of nonalgebraic functions, also called____________functions.

In Exercises \(1-3,\) fill in the blanks. You can consider log \(_{a} x\) to be a constant multiple of \(\log _{b} x ;\) the constant multiplier is _____ .

Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(4^{2 x-7}=64\) (a) \(x=5\) (b) \(x=2\)