Converting Logs to Exponents and Vice Versa

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

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CCSS.HSF.BF.B.5

Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

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CCSS.HSF.BF.B.5

Rewrite each logarithmic equation as an exponential equation and vise versa

Mathematical Equivalence

ON

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CCSS.HSF.BF.B.5

Match each logarithmic expression to its equivalent exponential form.

• e¹⁰ ≈ x

• ln x ≈ 10

• 5^x = 10

• log_x 5 = 10

• x¹⁰ = 5

• ln 10 ≈ x

• 10⁵ = x

• log x = 5

• e^x ≈ 10

• log₅ 10 = x

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CCSS.HSF.BF.B.5

Write 5^x =10 in log form

• x = log 5

• x = log₅10

• x = 5 log10

• x = 10 log 5

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CCSS.HSF.BF.B.5

Write 6^x = 8 in log form.

• log₆ 8 = x

• log₈ 6 = x

• log₆ x = 8

• log₈ x = 6

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CCSS.HSF.BF.B.5

Rewrite each logarithmic equation as an exponential equation and vise versa

Mathematical Equivalence

ON

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CCSS.HSF.BF.B.5

Simplify: 2log(x) + 3log(xy)

• log(x⁵y³)

• log(5xy)

• 5log(x²y)

• log(6x²y)