Algebra II - 8.1-8.2

Expotentiation

Raising a quantity to a power

“2^x = 8”

Log Expression

Another way to Define an EXPONENT

Logarithmic Function

log_b ^a = C

The LOG of the result with given base EQUALS THE EXPONENT

Exponential Function

B^c = a

A base RAISED to an exponent equals the result

Evaluating Logarithmic expression

log_b # = X; Solve with BOTH NUMBERS SAME BASE,

then solve for X in exponents

Inverse Logarithmic expression

Replace F(X) with Y

CHAGNE X AND Y

EXP - > LOG

LOG - > EXP

Then SOLVE FOR Y

10

The common base for any logarithmic function when NOT given is __ .

( )

If X and a # are GROUPED IN “__“ then its APART of the LOG,

Whereas if the number is NOT in “__ ” its NOT apart of the LOG

Transformations of Log functinos

f(X)= a x log_b(x - h) + k

Where X = Vertical Asmptote

Range = All real numbers

x = h

the VERTICAL ASYMPTOTE, used within log functions

Properties of logarithms

for POS NUMBERS; B, m, n with b ≠ 1

Product property

Log of a PRODUCT is the SUM OF THE LOGS

Log_bmn = log_bm + log_bn

(M and N separate off from multiplication to addition)

Quotient Property

the Log of a quotient is the DIFFERENCE of the LOGS

Log_b m/n = log_bm - log_bn

(M and N separate off from division to subtraction)

Power property

the Log of a number RAISED TO A POWER is the POWER MULTIPLED to the LOG of a number

log_bmⁿ = n log_bm

(the nth power of m, becomes multiplied to the log)

Expand

When logs BEGIN in a MULTIPLICATION or DIVISION form

Multiply - You’ll add the logs

Divide - You’ll subtract the logs

Condense

When you begin with an expression such as ADDITION or SUBTRACTION and convert the log to another form

Addition- you’ll be multiplying the exponents of the logs

Subtraction- you’ll divide the exponents of the logs

Logarithmic equation

An equation containing ONE or MORE logarithms