Inverse Functions and Logarithms

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

log₈(x) = 2

• x = 256

• x = 64

• x = 16

• x = 32

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)

• (-4, -1) and (-6, -4)

• (-1, -4) and (-4, -6)

• (4, 1) and (6, 4)

Understanding the relationship between exponential and logarithmic functions: Explain the relationship between the exponential function f(x) = 3^x and its corresponding logarithmic function

• They are inverse functions of each other.

• They have no relationship

• The exponential function is a subset of the logarithmic function

• They are parallel functions

Converting exponential to logarithmic form: Write the logarithmic form of the exponential equation 3^x = 27

• log3(3) = x

• log3(9) = x

• log27(3) = x

• log3(27) = x

Converting exponential to logarithmic form: Convert the exponential equation 5^2 = 25 to logarithmic form

• log2(25) = 5

• log5(2) = 25

• log25(5) = 2

• log5(25) = 2

Solving exponential equations using logarithms: Solve the equation 2^x = 16 using logarithms

• x = 4

• x = 8

• x = 10

• x = 2

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

Find the inverse of y=9^x

• y=log_x9

• y=log₁₀9

• x=log_y9

• y=log₉x

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e