Lesson on Base e and Natural Logarithms

Base e and Natural Logarithms

Solve the logarithm

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• ln(x) = 5

• e^ln(x) = e⁵

• x = e⁵ (Exact solution)

• x = 148.4132 (Approximate solution)

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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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Multiple Choice

Which of the following is the value of x given;
e^(x + 6) = 12

• x = ln 6

• x = -6 + ln12

• x = ln72

• x = ln(-2)

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

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 exact answer.

$$\ln\left(x\right)=3$$  

• x = e³

• x = e^x

• 3 = e^x

• 3 = e^-3