Exponential and Logarithmic functions

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

ln(e^W)

• e
• W
• e^W
• undefined

Solve for n:
2³ⁿ = 4

• 2
• 3
• 2/3
• 4

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)
• log₂(xy⁵)
• log₂(x/y)⁵
• log₂(x/5y)

Write log_b(x/y) as two logs

• log_bx-log_by
• log_bx+log_by
• log_bx*log_by
• log_bx/log_by

Solve:  7ⁿ⁺¹⁰−8 = 6

• -7.374
• -7.360
• -8.644
  
• -8.853

Suppose a culture of bacteria begins with 500 cells and dies by 30% each year. Write an equation that represents this situation.

• y = 500(0.7)ⁿ
• y = 500(1.3)ⁿ
• y = 500(1.7)ⁿ
• y = 500(1.13)ⁿ

Solve for x. Round to the nearest ten thousandth.
$4^{\left(x-3\right)}=9$

• 1.17

• 1.18

• 4.58

• 4.59

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions