IM3 Unit 5 Intro to Logs

Solve the exponential equation:

• -11/4
• 6
• 9/4
• 8

Write in logarithmic form.
2^-4 = ¹/₁₆

• log₂(¹/₁₆) = -4
• log_-4(¹/₁₆) = 2
• log _-4 2 = ¹/₁₆
• log₂(-4) = ¹/₁₆

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Write in exponential form.
log₂32 = 5

• 2^-5 = 32
• 2³² = 5
• 2⁵ = 32
• 32⁵ = 2

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• x = 125

• x = 5

• x = 7

• x = 4

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• 3.091

• 2.365

• 2.746

• 1.804

Rewrite in exponential form:
ln(2) = x

• 2^x = 10
• 10² = x
• e^x = 2
• e² = x

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• x = 3

• x = 2

• x = 6

• x = 4

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

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Solve: 9^8-x = 27^x-3

• x = 5
• x = -5
• x = 1/5
• x = -1/5

Rewrite e^x = 9 using a logarithm

• ln x = 9

• ln 9 = x

• log_x e = 9

• log₉ x = e

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