Intro Logarithmic Functions

Rewrite as an exponential:
log(10,000)=4.

• e⁴=10,000

• 4^10,000=10

• 10⁴=10,000

• 0⁴=10

Change to Exponential Form:
log₂₈₉ 17 = 1/2

• 289^1/2 = 17

• 17^1/2 = 289

• 289¹⁷ = 1/2

• 1/2¹⁷ = 289

10⁰ = 1

• log 1 = 0

• log 0 = 1

• log ₀ 10 = 1

• log ₀ 1 = 10

The function f(x) = log_bx is the ___________ function with base _________.

• exponential, b

• exponential, x

• logarithmic, b

• logarithmic, x

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Write log₃ 81 = 4 in exponential form.

• 81⁴=3

• 81³=4

• 4³=81

• 3⁴=81