Solving Exponential Equations

Solve Exponential Functions:

With Common Base

LT EL.2

Exponents

Labeling

Label the parts of the exponent:

Drag labels to their correct position on the image

Base

Exponent

What do you know about exponents?

​A power raised to a power-multiply the exponents

​When dividing, subtract exponents

Multiple Choice

$$x^5\ \cdot\ x^3$$

• $$x^{15}$$

• $$x^8$$

• $$x^2$$

• Can't be done

Multiple Choice

$$\left(x^6\right)^3$$

• 
  $$x^9$$

• $$x^{12}$$

• $$x^{15}$$

• $$x^{18}$$

Multiple Choice

$$\frac{x^8}{x^3}$$

• x^6
• x^5
• x^2
• x^4

​Solving with like bases

​If both exponents have the same base, set the exponents equal to each other and solve for x.

Multiple Choice

$$3^{\left(x+7\right)}=3^2$$

• x = -5
• x = 1
• x = 0
• x = 10

Multiple Choice

$$4^{2x}=4^{\left(-2x+8\right)}$$

• x=0

• x=-2

• x=2

• x=4

​Solving with unlike bases

​Step one: make the bases alike
Step two: solve like before

​What if I have a fraction for a base?

Multiple Choice

$$5^{\left(3x+1\right)}=25^{\left(x+1\right)}$$

• x = 2
• x = 1
• x = 0
• x = -1

Multiple Choice

$$\left(\frac{1}{4}\right)^{\left(x+3\right)}=16^x$$

• 0
• 3
• 2
• -1