4th 9 Weeks / Logarithms

The graph  $\log_7\left(x\right)+4$  is given. What is the domain?

•  $\left(-\infty,+\infty\right)$  

•  $\left(0,+\infty\right)$  

•  $\left(-\infty,+\infty\right)$  

•  $\left(0,-\infty\right)$  

 Find the inverse of the following $y=5^x-6$ 

•  $y=\log_5\left(x+6\right)$  

•  $y=\log_5\left(x\right)+6$  

•  $y=\log_5\left(x-6\right)$  

•  $y=\log_5x+6$  

The graph of a logarithmic function is given. Which of the following is the inverse of the function?

• 
• 
• 
• 

What is the vertical asymptote of the given function?

 $f\left(x\right)=\log\left(x+6\right)-2$  

•  $x=6$  

•  $x=-6$  

•  $x=2$  

•  $x=-2$  

Which of the following describes the asymptote behavior of the following function

 $f\left(x\right)=\log\left(x\right)$  

Hint: Graph it, trace it from the right, where does it go to?

• As x approaches 0 from the right, it approaches negative infinity

• As x approaches 0 from the right, it approaches positive infinity

• As x approaches 0 from the right, it approaches the moon

• As x approaches 0 from the right, it approaches the galaxy

Rewrite the following exponential equation into a log equation.

 $20=5\left(3\right)^x-5$  

 $\left(x=b^y\ iff\ \log_bx=y\right)$  

•  $\log_35=x$  

•  $\log_{15}25=x$  

•  $\log_3x=5$  

•  $\log_x5=3$  

Find the inverse of the following $y=\log_6x$ 

•  $6^y=x$  

•  $6^x=y$  

•  $y^6=x$  

•  $x^6=y$  

Find the value of x given the following

 $\log_x3=\frac{1}{4}$  

•  $x=\left(3\right)^{\frac{1}{4}}$  

•  $x=3\left(\frac{1}{4}\right)$  

•  $x=9$  

•  $x=81$