Solving Exponential and Logarithmic Equations

7.5 - Exponential and Logarithmic Equations

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Objective

To solve 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

Example 3

You try

Math Response

Solve $$32=2^{\left(2x-9\right)}$$  

Type answer here

Correct Answer: x=7

Deg^°

Rad

Logarithmic Equation

An equation with a logarithmic expression that contains a variable.

To solve a logarithmic equation

Example 1

Example 2

Another way to think about that problem

Example 3

You try

Math Response

Solve  $$2\log_{ }x-\log_{ }4=2$$  

Type answer here

Correct Answer: x=20

Deg^°

Rad

Multiple Choice

Solve:

log₂ x + log₂ (x + 5) = log₂ (3x + 8)

• x = 2

• x = -4

• x = 2 and x = -4

• no solution

Multiple Choice

Solve:

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

Multiple Choice

Solve the equation: 

$$6^{2x}=6^{\left(-x-1\right)}$$  

• $$-\frac{1}{3}$$  

• $$\frac{15}{8}$$  

• $$5$$  

• $$\frac{19}{10}$$  

Multiple Choice

Solve 2.8^x = 41

• 0.277

• 3.607

• -0.282

• 3.684

Poll

Select the image that most closely reflects how well you think you can solve exponential and logarithmic equations: