Using Properties of Exponents to Solve Exponential Equations (5.4.1)

Question 1

• Exponential equations are equations where the variable is in the exponent.

Answer 1

• Exponential equations are equations where the variable is in the exponent.

Question 2

• Steps for Solving an Exponential Equation By Using Properties of Exponents

1. Use properties of exponents to write each side of the equation as a power with a common base.
2. Set the expressions in the exponents equal to each other and solve for the variable.

Answer 2

• Steps for Solving an Exponential Equation By Using Properties of Exponents

1. Use properties of exponents to write each side of the equation as a power with a common base.
2. Set the expressions in the exponents equal to each other and solve for the variable.

Question 3

• Review of the Properties of Exponents
Power of a Product Property: (ab)^x = (a^x)(b^x)
Power of a Power Property: (a^x)^y = a^x ^y
Product of Powers with Common Bases Property: (a^x)(a^y) = a^(x + y)
Quotient of Powers with Common Bases Property: a^x/a^y = a^(x – y)
Negative Power Property: (a/b)^–x = (b/a)^x

Answer 3

• Review of the Properties of Exponents
Power of a Product Property: (ab)^x = (a^x)(b^x)
Power of a Power Property: (a^x)^y = a^x ^y
Product of Powers with Common Bases Property: (a^x)(a^y) = a^(x + y)
Quotient of Powers with Common Bases Property: a^x/a^y = a^(x – y)
Negative Power Property: (a/b)^–x = (b/a)^x