Exprese como un logaritmo = 1 / 3 log a(x2 - 1) - log aY - 4logaZ?

Logarithmic Functions

y = logax x = a

y

(exponential form)

Properties of Logarithms

1.

Loga1 = 0 because a0 = 1

2.

Logaa = 1 because a1 = a

3.

Logaa

x = x and = x Inverse Property

4.

If logax = logay then x = y One - to - one

Natural Logarithms

y = lnx if x = e

y

Properties of Logarithms

1.

Ln1 = 0 because e0 = 1

2.

Lne = 1 because e1 = e

3.

Lnex = x and elnx = x inverse properties

4.

If lnx = lny then x = y one - to - one

Logarithmic Properties

1.

Product—loga(xy) = logax + logay

2.

Quotient—loga(x / y) = logax - logay

3.

Power—logax

y = ylogax

Natural Logarithmic Properties

1.

Product—ln(xy) = lnx + lny

2.

Quotient—ln(x / y) = lnx - lny

3.

Power—lnxy = ylnx

Change of Base

Base b

logax = logbx

logba

Base 10

logax = log10x

log10a

Base e

Logax = lnx

lna.