Lesson on Base e and Natural Logarithms

Base e and Natural Logarithms (4/5/22)

Mr. Suarez (Algebra 2)

EX #1: Solve the logarithm

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EX #1: Solve the logarithm

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• ln(x) = 5

EX #1: Solve the logarithm

​

• ln(x) = 5

• e^ln(x) = e⁵

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EX #1: Solve the logarithm

​

• ln(x) = 5

• e^ln(x) = e⁵

• x = e⁵ (Exact solution)

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EX #1: Solve the logarithm

​

• ln(x) = 5

• e^ln(x) = e⁵

• x = e⁵ (Exact solution)

• x = 148.4132 (Approximate solution)

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Multiple Choice

Solve the following logarithm to find the exact answer.

$$\ln\left(x\right)=3$$  

• x = e³

• x = e^x

• 3 = e^x

• 3 = e^-3

Multiple Choice

Solve the following logarithm to find the approximate answer.

Round to 4 decimal places.

$$\ln\left(x\right)=3$$  

• x = 20.0855

• x = 0.0498

• x = 3

• x = 0.3333

Multiple Choice

Solve the following logarithm to find the exact answer.

$$\ln\left(x\right)=\frac{1}{2}$$  

• x = e^1/2

• x = e^-2

• 1/2 = e^x

• 2 = e^-1/2

Multiple Choice

Solve the following logarithm to find the approximate answer.

Round to 4 decimal places.

$$\ln\left(x\right)=\frac{1}{2}$$  

• x = 1.6487

• x = -1.6487

• x = 1/2

• x = 2

Multiple Choice

Solve the following logarithm to find the exact answer.

$$\ln\left(x\right)=-4$$  

• x = e^-4

• x = e⁴

• 4 = e^x

• 1/4 = e^-4

Multiple Choice

Solve the following logarithm to find the approximate answer.

Round to 4 decimal places.

$$\ln\left(x\right)=-4$$  

• x = 0.0183

• x = 1.0183

• x = 1/4

• x = -4

EX #2: Solve the logarithm​

• ln(x + 15) = 3

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EX #2: Solve the logarithm​

• ln(x + 15) = 3

• e^{ln(x + 15)} = e³

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EX #2: Solve the logarithm​

• ln(x + 15) = 3

• e^{ln(x + 15)} = e³

• x + 15 = e³

  -15 -15

EX #2: Solve the logarithm​

• ln(x + 15) = 3

• e^{ln(x + 15)} = e³

• x + 15 = e³

  _ -15 -15

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• x = e³ - 15

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EX #2: Solve the logarithm​

• ln(x + 15) = 3

• e^{ln(x + 15)} = e³

• x + 15 = e³

  __-15 -15

• x = e³ - 15

• x = e³ - 15 (Exact solution)

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EX #2: Solve the logarithm​

• ln(x + 15) = 3

• e^{ln(x + 15)} = e³

• x + 15 = e³

  __-15 -15

• x = e³ - 15

• x = e³ - 15 (Exact solution)

• x = 5.0855 (Approximate solution)

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