Precalculus (MAC1140) Section 3.2 Handout

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Precalculus (MAC1140) Section 3.2 Handout

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Precalculus (MAC1140) Section 3.2 Handout

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Precalculus (MAC1140) Section 3.2 Handout

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Precalculus (MAC1140) Section 3.2 Handout

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Precalculus (MAC1140) Section 3.3 Handout

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Precalculus (MAC1140) Section 3.3 Handout

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Precalculus (MAC1140) Section 3.3 Handout

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Precalculus (MAC1140) Section 3.4 Handout

In this section we solve exponential and logarithmic equations. To simplify this, it is broken down to three types of equations you may encounter and a general approach to solving each. 1. 𝒂𝒇(𝒙) = 𝒃 Solve by taking the logarithm (or natural logarithm) of both sides. 2. 𝐥𝐨𝐠𝒂 𝒇(𝒙) = 𝒃 Solve by changing to exponential form 𝑎 = 𝑓(𝑥). 3. 𝐥𝐨𝐠𝒂 𝒇(𝒙) = 𝐥𝐨𝐠𝒂 𝒈(𝒙) The given equation is equivalent to the equation 𝑓(𝑥) = 𝑔(𝑥). Solve algebraically. In the following examples identify the type of equation you are given, and then use the appropriate method to solve. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution.

Example:

5 3 = 1166

Example:

𝑒2 − 8𝑒 + 15 = 0

Example:

6 1 = 42 1

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Precalculus (MAC1140) Section 3.4 Handout

In the following examples identify the type of equation you are given, and then use the appropriate method to solve. Express solutions in exact form.

Example:

ln(𝑥 − 4) + ln(𝑥 + 1) = ln(𝑥 − 8)

Example:

log4[(3𝑥 + 8)(𝑥 − 6)] = 3

Precalculus (MAC1140) Section 3.4 Handout

Try These!! log(2𝑥 − 1) = log(𝑥 + 3) + log 3 log2(𝑥 − 7) + log2 𝑥 = 3

Precalculus (MAC1140) Section 3.4 Handout