Unit 3 Exam Review

Determine the domain of $$g\left(x\right)=\log_3\left(4x-2\right)$$ ?

Use properties of the logarithms to simplify the expression below into a single logarithm. Assume that all variables represent positive real numbers. $$5\log_3X-\log_3Y+\frac{1}{5}\log_3Z$$

Simplify: $$\log_216+\log_28$$

Consider a function g(x) such that $$\lim_{x\rightarrow-\infty}\ g\left(x\right)=\infty$$ and $$\lim_{x\rightarrow\infty\ }g\left(x\right)=0$$ . Which of the following functions could be g(x)?

Determine the following statement that best describes the transformation of the graph of the parent function $$f\left(x\right)=\log\ x$$ into the graph of $$g\left(x\right)=\log_{ }\left(\frac{1}{2}x-4\right)+3$$ ?

How many solutions are there to the following logarithmic equation?

$$\log_3\left(x+1\right)+\log_3\left(x-2\right)=\log_39$$

Determine the following that best describes the graph of $$f\left(x\right)=e^{-x}+4$$ ?

Evaluate the properties of logarithms to expand the expression below into multiple logarithms. Assume that all variables represent positive real numbers. $$\ln\left(\frac{\sqrt[4]{x}}{y^8}\right)$$

What is the inverse function of $$f\left(x\right)=6^x$$ ?

Let $$g\left(x\right)=3^{-x}+5$$ , determine which of the following about g(x) must be true? I. The graph of g(x) is increasing on (-∞, ∞). II. There are no local or absolute extrema on the graph of g(x). III. The graph is bounded below.