5.4 Logarithms

5.4 Logarithms

Eq: What are logarithms and how are they evaluated?

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The base of $$x^4$$ is​ ​

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and the exponent is ​

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.

The base of $$23^{12}$$ is ​

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​ and the exponent is ​

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.

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The base of​ $$\left(12x\right)^4$$ is ​

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and the exponent is ​

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.

The base of $$13x^{10}$$ is ​

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and the exponent is ​

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.

What's going on here? Think about the pattern.

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What's going on here? Type/draw your response.

Multiple Choice

Rewrite in exponential form:

log₉x=2

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

Multiple Choice

Write 6^x = 8 in log form.

• log₆ 8 = x

• log₈ 6 = x

• log₆ x = 8

• log₈ x = 6

Math Response

Write 5^x =10 in log form

Type answer here

Correct Answer: \log_5\left(10\right)=x

Deg^°

Rad

Math Response

Rewrite log₃t = 5 in exponential form.

Type answer here

Correct Answer: 3^5=t

Deg^°

Rad

Math Response

Rewrite log_bc = a in exponential form.

Type answer here

Correct Answer: b^a=c

Deg^°

Rad

Draw

Create your own example below.

log_by = x

The logarithm with a base b of the result (or argument) is equal to the exponent.

ex: log₃81 = 4

Logarithmic Form

b^x = y

The base raised to the exponent is equal to a result.

ex: 3⁴ = 81

Exponential Form

Logarithm Rule