Transforming Logarithms

• True, subtraction between two logarithms is division in condensed form.

• True, a logarithm is an exponent. When dividing like bases you subtract exponents therefor dividing logarithms as in this example.

• False, subtraction between two logarithms is division within a single logarithm in condensed form.

Condense: log6 + logx

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Solve the equation for x.

• 32

• 25

• 1.66

• 512

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CCSS.HSF.BF.B.5

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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CCSS.HSF.BF.B.5

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

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CCSS.HSF.BF.B.5

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁3 = 4

• log₃81 = 4

• log₄81 = 3

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CCSS.HSF.BF.B.5

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Write as a single logarithm:

log(30)-log(6)

• -6log(30)

• log(24)

• log(-24)

• log(5)

Rewrite in exponential form:
ln(2) = x

• 2^x = 10

• 10² = x

• e^x = 2

• e² = x

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CCSS.HSF.BF.B.5