Exponents and Logarithms Test

Which of the following expressions is equivalent to  $6\log\left(x\right)-2\log\left(y\right)?$  

•  $\log\left(x^6+y^2\right)$  

•  $\log\left(\frac{6x}{2y}\right)$  

•  $\log\left(\frac{x^6}{y^2}\right)$  

•  $\log\left(x^6\cdot y^2\right)$  

Solve the following equation for x:  $\log_5\left(x+13\right)=2$  

•  $x=12$  
  

•  $x=38$  

•  $x=19$  

•  $x=-3$  

Which exponential function best represents the graph?

• 
  

  $y=20\cdot\left(2\right)^x$
  

• $y=2\cdot\left(x\right)^5$

• $y=20\cdot\left(-2\right)^x$

• $y=20\cdot\left(\frac{1}{2}\right)^x$

If  $\log_4\left(a-2\right)=2$  , then a =

• 14
  

• 10

• 18

• 6

Which equation is equivalent to

 $\log_4\left(\frac{1}{2}\right)=x$  ?

•  $4^{\frac{1}{2}}=x$  

•  $\left(\frac{1}{2}\right)^4=x$  

•  $4^x=\frac{1}{2}$  

•  $\left(\frac{1}{2}\right)^x=4$  

If the parent function is: $f\left(x\right)=\log_2\left(x\right)\$ , what are the transformations that happen to the transformed function:  $g\left(x\right)=\log_2\left(x+6\right)-2$  ?

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What rule states that:

 $\log\left(x^c\right)=y\ \ \longrightarrow\ c\cdot\log\left(x\right)=y$  

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Simplify:

 $4^a\cdot4^b$  

•  $4^{\left(a\cdot b\right)}$  

•  $4^{\left(a+b\right)}$  

•  $4^{\left(a-b\right)}$  

•  $\left(4^a\right)^b$  

Which exponential function best represents the graph?

• 
  

  $y=40\cdot\left(2\right)^x$
  

• $y=10\cdot\left(2\right)^x$

• $y=10\cdot\left(\frac{1}{2}\right)^x$

• $y=2\cdot\left(x\right)^{10}$

Which of the following represent exponential growth? Check ALL that apply.

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