Solving Exponential Equations Using Properties

Rewrite in Logarithmic Form:

5^x = 125

• log ₅ 125 = x

• log _x 125 = 5

• log ₅ x =125

• log₁₂₅ x = 5

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CCSS.HSF.BF.B.5

• 3.9

• 4.5

• 5.3

• 10.1

Rewrite in logarithmic form

• log ₇ 20 = x+2

• log ₇ 20 = x

• log ₂₀ x+2 = 7

• log _x+2 20 = 7

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CCSS.HSF.BF.B.5

Solve for x

• log ₇ (20) - 2 = x

• log ₇ (22) = x

• log₅ (20) = x

• log ₇ (18) = x

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CCSS.HSF.BF.B.5

Isolate the base/exponent.

• 6^x = 12

• 3^x = 24

• 2^x = 4

• 3^x = 6

Rewrite in logarithmic form

• log₃ 6 = x

• log₆ 3 = x

• log_x 6 = 3

• log₆ x = 3

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CCSS.HSF.BF.B.5

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CCSS.HSF.BF.B.5

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CCSS.HSF.LE.A.4

A new car is purchased for $23700. The value of the car depreciates at 13% per year. Which equation models the value of the car after t years?

• y = 23700(1 - 13)^t

• y = 23700(1 - 1.3)^t

• y = 23700(1 - .13)^t

• y = 23700(1 + .13/1)^t

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CCSS.HSF.LE.A.2

A new car is purchased for $23700 dollars. The value of the car depreciates at 13% per year. To the nearest year, how long will it be until the value of the car is $8000?