Final Exam Review Part II

The exponential function f with base b is defined by  $f\left(x\right)=$ ______, where  $b>0\ and\ b\ne1.$   

•  $b^x$  

•  $x^b$  

The graph of the exponential function f with base b approaches, but does not touch, the ____-axis.

• x

• y

• z

Use the compound interest formula  $A=P\left(1+\frac{r}{n}\right)^{nt}$  to solve the given problem. Round answer to the nearest cent. Find the accumulated value of an investment of $15,000 for 4 years at an interest rate of 5% if the money is compounded semiannually.

The equation  $y=\log_bx$  is equivalent to the exponential form ______, where  $x>0,\ b>0,\ b\ne1.$  

•  $b^x=y$  

•  $b^y=x$  

•  $x^b=y$  

•  $y^x=b$  

•  $x^y=b$  

Fill in the blank so that the resulting statement is true. $\log_bb=$ ______ 

The product rule for logarithms states that  $\log_b\left(MN\right)=$ ______. 

•  $\log_bM+\log_bN$  

•  $\log_bM-\log_bN$  

If  $b^M=b^N$  , then _______.

• M = N

• b = N

• b = M

Decide whether the statement is true or false.
 $x^4=15$   is an exponential equations.

• True, because the equation contains a variable raised to a power.

• False, because only one term contains an exponent.

• True, because there is an exponent in the equation.

• False, because there is no variable in the exponent.

Determine whether the statement is true or false.
 $-41$  is a solution of  $\log_3\left(x+50\right)=2.$  

• False, because  $-41+50\ne2^3.$  

• True, because  $-41+50>0$  and logarithms are defined for positive numbers.

• True, because  $-41+50=3^2.$  

• False, because the logarithm of a negative number is not defined.

A solution to a system of linear equations in two variables is an ordered pair that _____________.

• satisfies an equation in the system.

• satisfies both equations in the system.

• does not satisfy either equation in the system.