8.3-4 – logarithmic functions
DESCRIPTION
8.3-4 – Logarithmic Functions. Logarithm Functions. Logarithm Functions If log b x = y ,. Logarithm Functions If log b x = y , then b y = x. Logarithm Functions If log b x = y , then b y = x . Ex. 1 Write the following in exponential form. a. log 8 1 = 0. - PowerPoint PPT PresentationTRANSCRIPT
8.3-4 – Logarithmic Functions
Logarithm Functions
Logarithm Functions
If logbx = y,
Logarithm Functions
If logbx = y, then by = x.
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
logbx = y
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
logbx = y
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
logbx = y
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
logbx = y
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
logbx = y
by = x
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
logbx = y by = x 80 = 1
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0
logbx = y by = x 80 = 1
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0 b. log2(1/16) = -4
logbx = y by = x 80 = 1
Logarithm Functions
If logbx = y, then by = x.
Ex. 1 Write the following in exponential form.
a. log81 = 0 b. log2(1/16) = -4
logbx = y 2-4 = 1/16 by = x 80 = 1
Logarithm Functions
If logbx = y, then by = x.Ex. 1 Write the following in exponential form.
a. log81 = 0 b. log2(1/16) = -4
logbx = y 2-4 = 1/16 by = x 80 = 1
Ex. 2 Write the following in logarithmic form.a. 103 = 1000 b. 27⅓ = 3
Logarithm Functions
If logbx = y, then by = x.Ex. 1 Write the following in exponential form.
a. log81 = 0 b. log2(1/16) = -4
logbx = y 2-4 = 1/16 by = x 80 = 1
Ex. 2 Write the following in logarithmic form.a. 103 = 1000 b. 27⅓ = 3 by = x
Logarithm Functions
If logbx = y, then by = x.Ex. 1 Write the following in exponential form.
a. log81 = 0 b. log2(1/16) = -4
logbx = y 2-4 = 1/16 by = x 80 = 1
Ex. 2 Write the following in logarithmic form.a. 103 = 1000 b. 27⅓ = 3 by = x
Logarithm FunctionsIf logbx = y, then by = x.
Ex. 1 Write the following in exponential form.a. log81 = 0 b. log2(1/16) = -4 logbx = y 2-4 = 1/16
by = x 80 = 1
Ex. 2 Write the following in logarithmic form.a. 103 = 1000 b. 27⅓ = 3 by = x logbx = y
Logarithm FunctionsIf logbx = y, then by = x.
Ex. 1 Write the following in exponential form.a. log81 = 0 b. log2(1/16) = -4 logbx = y 2-4 = 1/16
by = x 80 = 1
Ex. 2 Write the following in logarithmic form.a. 103 = 1000 b. 27⅓ = 3 by = x logbx = y
log101000 = 3
Logarithm FunctionsIf logbx = y, then by = x.
Ex. 1 Write the following in exponential form.a. log81 = 0 b. log2(1/16) = -4 logbx = y 2-4 = 1/16
by = x 80 = 1
Ex. 2 Write the following in logarithmic form.a. 103 = 1000 b. 27⅓ = 3 by = x log273 = ⅓ logbx = y
log101000 = 3
Ex. 3 Evaluate each expression.
a. log264 b. log164
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y
logbx = y
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y
logbx = y
by = x
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y
logbx = y
by = x
2y = 64
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y
logbx = y
by = x
2y = 64
2y = 26
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y
logbx = y
by = x
2y = 64
2y = 26
y = 6
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y
logbx = y
by = x
2y = 64
2y = 26
y = 6
Ex. 3 Evaluate each expression.
a. log264 b. log164
log264 = y log164 = y
logbx = y 16y = 4
by = x (42)y = 4
2y = 64 42y = 41
2y = 26 2y = 1
y = 6 y = ½
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
logbx = y
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
logbx = y
by = x
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
logbx = y
by = x
92 = x
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
logbx = y
by = x
92 = x
81 = x
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
logbx = y
by = x
92 = x
81 = x
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
logbx = y b2 = 121
by = x b = ±11
92 = x
81 = x
Ex. 4 Solve each equation.
a. log9x = 2 b. logb121 = 2
logbx = y b2 = 121
by = x b = ±11
92 = x b = +11
81 = x *b cannot be neg.!