Natural Logarithms

Expand ln(4x)

• ln4 + lnx

• ln 4 - lnx

• ln4x

• ln 4 - x

Expand ln(uw²)

• ln u + ln w

• 2ln uw

• ln u + 2ln w

• ln (uw) + 2

Expand ln(xyz)

• ln x + ln y

• ln x + yz

• lnx + ln y + z

• lnx + lny + lnz

The natural logarithm has what base?

• 10

• 0

• e

• -e

Rewrite e^x = 9 using a logarithm

• ln x = 9

• ln 9 = x

• log_x e = 9

• log₉ x = e

Rewrite in exponential form:
ln(2) = x

• 2^x = 10

• 10² = x

• e^x = 2

• e² = x

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions