Logarithmic and Exponential Properties

 $\log_6\left(x+4\right)=\ \log_6\left(2x-5\right)$  

Solve the given equation:

• {-9)

• (9)

• (-1}

• ()

 $e^{4x}=\ 5$  

Solve the given equation:

•  $x=\frac{\ln e}{4}$  

•  $x=\frac{4}{5}$  

•  $x=\frac{\ln\ \left(4\right)}{5}$  

•  $x=\frac{\ln\left(5\right)}{4}$  

 $y=\log\left(3x-9\right)$  

Find the domain of the function:

•  $x\in\left(-\infty,3\right]$  

•  $x\in\left(-\infty,3\right)$  

•  $x\in\left[3,+\infty\right)$  

•  $x\in\left(3,+\infty\right)$  

 $\log\left(x-1\right)+\log\left(x+1\right)=\log\left(3\right)$  

Solve for x

•  $x=\left\{-2,2\right\}$  

•  $x=\left\{2\right\}$  

•  $x\ =\left\{\sqrt{1001}\right\}$  

•  $x=\left\{\right\}$  

 $2\log_5y\ -\ \frac{1}{2}\log_5x$ 

Write it as a single expression

•  $\frac{\log_5y}{2\log5x}$  

•  $\log_5\left(\frac{y^2}{\sqrt{x}}\right)$  

•  $\log_5y^2+\log_5\sqrt{x}$  

•  $\log_5\left(\frac{y^2}{2x}\right)$  

What is the vertical asymptote for the graph of :

y = ln (7 - 14x)

• $x\ =\ 2$

• $x\ =-\ \frac{1}{2}$

• $x\ =\frac{1}{2}$

• $y\ =\ \frac{1}{2}$

Write the logarithmic equation in the exponential form:

log (x-2) = -1

• $10^{-1}=\ x-2$

• $10\ ^x-2\ =-1$

• $\ln\ \left(x-2\right)\ =-1$

• $\left(x-2\right)^{-1}=10$

 $5^{\left(x+1\right)}=7$ 

 Write the exponential equation as a logarithmic form

•  $\log_5\left(x+1\right)=7$  

•  $\log_7\left(x+1\right)\ =5$  

•  $\log_5\left(7\right)=x\ +1$  

•  $\log_7\left(5\right)=\ x+1$  

 $f\left(x\right)\ =\ e^{\left(2x-5\right)}-9\$  

Write the domain of the function:

•  $x\in\left(-\infty,+\infty\right)$  

•  $x\in\left(-\infty,\frac{5}{2}\right)$  

•  $x\in\left(\frac{5}{2},+\infty\right)$  

•  $x\in\left(-9,+\infty\right)$  

 $m\left(x\right)\ =e^{\ 7x\ }-8$  

Determine the horizontal asymptote of the function:

•  $y\ =7x$  

•  $y\ =\ 8$  

•  $y=-\ 8$  

•  $y=\ 0$