Weeks 27/28 Exponential and Logarithmic Equations

EXPONENTIAL AND LOGARITHMIC

EQUATIONS

Exponential Equation

An equation containing one or more expressions that have a variable as an exponent

To solve exponential equations:

• Try writing them so the bases are the same

• Take the log of both sides

Example 1

Example 2

Logarithmic Equation

An equation with a logarithmic expression that contains a variable.

To solve a logarithmic equation

Example 1

Another way to think about that problem

Example 2

• 4x + 5 = 5x + 1

• 4 = x

Multiple Choice

4^{3x + 5} = 16

• -5/3

• -1

• -3/2

• 2/3

Multiple Choice

Solve the equation:  $$5^{\left(2-3x\right)}=25$$  

• $$\frac{7}{5}$$  

• $$-\frac{3}{4}$$  

• $$-\frac{7}{6}$$  

• $$0$$  

Multiple Choice

Solve:

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

Multiple Choice

Solve:

log₂(2) + log₂(8x) = 6

• x = 3

• x = 2

• x = 6

• x = 4

Multiple Choice

Solve:

log₃(x - 5) = 2

• 25

• 5

• 130

• 14

Multiple Choice

Rewrite log_pt = m in exponential form.

• p^t = m

• t^m = p

• m^t = p

• p^m = t

Multiple Choice

Write the exponential equation as a logarithm
6³=216

• log₆(3) = 216

• log₃(6) = 216

• log₆(216)=3

• log₂₁₆(6)=3

Multiple Choice

Solve for x.  $$3^{\left(x-7\right)}-3=24$$  

• 3

• 8

• 10

• No solution

Multiple Choice

Solve the following exponential equation: $$5^{-3x}=125$$  

• $$x=-1$$  

• $$x=-4$$  

• $$x=-3$$  

• $$x=1$$  

Multiple Choice

log(x+6) = 1

• 4

• 4.222

• -5

• -9.550

Multiple Select

Solve

$$\log_2\left(2x^2+8x-11\right)=\log_2\left(2x+9\right)$$  

• -5

• -2

• 2

• 5