Natural Logarithmic functions and Equations

The natural logarithm  𝑓(𝑥)=ln⁡(𝑥) is the same as which of the following?

• ln₁₀ x

• ln_e x

• log_e x

• log₁₀ x

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

The Natural Logarithm, abbreviated "ln" is log base ______

For the logarithm log⁡(17), what is the base of the logarithm? The base is ______

Write the logarithmic equation exponential form. 

log​₂ ​16=4 is the same as _______⁴

• 4¹⁶ = 2

• 2¹⁶ = 4

• 2⁴= 16

• None of these

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Write the logarithmic equation exponential form.  3⁵ = y

• log₃ y = 5

• log₅ y = 3

• log y = 243

• log₃ 5 = y

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Simplify/condense the logarithm  log⁡(4)+2⋅log⁡(𝑥)  into a single logarithm.

Solve the following logarithmic equation for x.

  log⁡₅ (2𝑥−8)=log⁡₅ (4𝑥−10)

x = ______ 

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

Solve the following logarithmic equation for x.

3 ln (x+4)=6. (Round your answer to the nearest hundredths

x = _____

The logarithm is the inverse function to  𝑥² . 

• True

• False

Tags

CCSS.HSF.BF.B.4

Which of the following is equivalent to ln (5x + 3) = 18 when solved for x?

• x = (e³ + 18)/5

• x = (e¹⁸ + 3)/5

• x = (e¹⁸ - 3)/5

• x = (10¹⁸ - 3)/5

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4