Exam 10: Inverse, Exponential, and Logarithmic Functions

The population growth of an animal species is described by $F(t)=700+70 \log _{3}(2 t+1)$ where $t$ is measured in months. Find the population of this species in an area 4 month(s) after the species is introduced.

Evaluate the logarithm. - $\log _{7}\left(\frac{1}{343}\right)$

What is the range of the function $y=\left(\frac{1}{2}\right)^{x}$ ?

Find the logarithm. Give an approximation to four decimal places - $\log \mathrm{e}$

If a number has a negative natural logarithm, then the number must be

Write in exponential form. - $\log _{2} \sqrt{2^{6}}=x$

What is the difference between $\ln$ a and $\log a$ ?

The space (in $\mathrm{m}^{3}$ ) in a landfill decreases with time as given by the function $F(t)=260-60 \log _{5}(4 t+1)$ , where $t$ is measured in years. How much space is left when $t=1$ ?

When solving a logarithmic equation, why must you not automatically reject all negative solutions?

Solve the equation. Give the solution to three decimal places. - $5^{-5 x-3}=24$

Graph the function. - $f(x)=4 x-2$

Evaluate the logarithm. - $\log _{10}\left(\frac{1}{1000}\right)$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f(x)=-\sqrt{x+3}$

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR. -Given $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$ , evaluate $\log _{10} 72$ .

Solve the equation. Give the exact solution - $2^{x}=\frac{1}{16}$

Why can the equation $\log _{4}(x-6)=\log _{4}(6-x)$ be said to have no solution?

Write in exponential form. - $\log _{5} x=0$

Solve the equation. Give the solution to three decimal places. - $4^{\mathrm{X}}=24$

Graph the given logarithmic function. - $y=\log _{4} x$

Find the indicated value. -Let $f(x)=2^{x} \cdot f(-3)$