Math 3H week 4: 16.1-16.2

Which expression is equivalent to  $\log_432$ ?

•  $\log_464-\log_432$  

•  $\frac{\log_464}{\log_42}$  

•  $\frac{\log_232}{\log_24}$  

• none of the above

Which expression is equivalent to  $\log_4\left(x^{2\ }+10x+25\right)$ ?

•  $\log_2\left(x+5\right)$  

•  $2\log_4\left(x+5\right)$  

•  $\frac{1}{2}\log_4\left(x+5\right)$  

• none of the above

Which of the following expression(s) is equivalent to  $81^{\frac{3}{4}}$ ?  (Select all that apply)

• 
• 
• 
• 

Which of the following logarithmic expression is equivalent to $\log_63+\log_612$ ? (Select all that apply)

• $\log_472-\log_49$

• $-\log_{\frac{1}{2}}4$

• $\log_354-\log_32$

• $\log_43+\log_43.2-\log_40.6$

• $2\log_34-\log_3\left(\frac{4}{9}\right)-\log_36$

Which of the following logarithmic expression(s) is equivalent to  $\frac{1}{2}\log_2\left(x^{2\ }-4x+4\right)$ ? (Select all that apply)

•  $\log_2\left(x^{2\ }-4\right)-\log_2\left(x-2\right)$  

•  $\log_2\left(x^{2\ }-4\right)-\log_2\left(x+2\right)$  

•  $\log_2\left(x^{2\ }-4x+4\right)$  

•  $\log_4\left(x^{2\ }-4\right)+\log_2\left(x-2\right)$  

•  $\log_4\left(x^{2\ }-4\right)^2-\log_2\left(x+2\right)$  

In solving the exponential equation  $2^{\left(x+3\right)}+1=5$ , what does  $x+3$  equal 

• 2

• 4

• 6

• none of the above

The graph shown can be used to solve the equation $3^x=4$ .  Which of the following is/are true? (select all that apply)

• the solution is  $x\approx1.26$  

• The input of the intersection point is the solution of the equation.

• The output of the intersection point is the solution of the equation.

• the solution is  $x=\frac{3}{4}$  

Which of the following equations can be solved using the Equality of Bases Property? (select all that apply)

• $2^x=17$

• $2^x=64$

• $\left(\frac{1}{3}\right)^x=27$

• $64^{\left(2x\right)}=\frac{1}{16}$