Convert Between Logs and Exponential Functions

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

Rewrite log_b(xⁿ)

• nlog_bx

• (log_bx)ⁿ

• xⁿlog_bx

• log_b(xⁿ)

Rewrite each logarithmic equation as an exponential equation and vise versa

Mathematical Equivalence

ON

Rewrite each logarithmic equation as an exponential equation and vise versa

Mathematical Equivalence

ON

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

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

• ln(wvu⁵)
• ln(u + v + w⁵)
• ln(uvw⁵)
• ln(uvw)⁵

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

Rewrite log_pt = m in exponential form.

• p^t = m

• t^m = p

• m^t = p

• p^m = t

log (3²) =?

• log 6

• 2 log 3

• log₂ 3

• log₃ 2