Converting from Logarithmic to
Exponential Form
Converting from Logarithmic to
Exponential Form
A logarithm is an exponent. That is, …
loga y = exponent to which the base a must be raised to obtain y
In other words, loga y = x is equivalent to ax = y
Example 1 Write the logarithmic equation log3 (9) = 2 in
equivalent exponential form.
(
)
=
Converting from Logarithmic to
Exponential Form
loga y = x is equivalent to ax = y
Example 2 Write the logarithmic equation C = logH (A) in
equivalent exponential form.
=(
)
Converting from Logarithmic to
Exponential Form
Common Logarithm: log10 y = log y
Example 3 Write the logarithmic equation log (10,000) = 4 in
equivalent exponential form.
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)
Converting from Logarithmic to
Exponential Form
Natural Logarithm: loge y = ln y
(Note: e 2.718)
Example 4 Write the logarithmic equation A = ln (19) in
equivalent exponential form.
(
)
=
Converting from Exponential to
Logarithmic Form
Converting from Exponential to
Logarithmic Form
loga y = x is equivalent to ax = y
Example 1 Write the exponential equation 8 = 23 in equivalent
logarithmic form.
log
(
)=
Converting from Exponential to
Logarithmic Form
loga y = x is equivalent to ax = y
Example 2 Write the exponential equation MK = D in equivalent
logarithmic form.
log
(
)=
Evaluating Logarithms
Evaluating Logarithms
loga y = exponent to which the base a must be
raised to obtain y
Note: loga y = x is equivalent to ax = y
Example 1 Determine the value of the logarithmic expression.
(a)
log2 16 =
(b)
log 100 =
(c)
ln e =
Evaluating Logarithms
Properties of Exponents:
a0 = 1, a 0
-m
a
1
= m
a
1
a
-m
= am
Example 2 Determine the value of the logarithmic expression.
(a)
ln 1 =
(b)
log 3
(c)
log1/2 2 =
1
=
81
Evaluating Logarithms
Properties of Exponents:
a0 = 1, a 0
-m
a
1
= m
a
1
a
-m
= am
a1/2 = a
Example 3 Determine the value of the logarithmic expression.
(a)
log 6 6 =
(b)
log 0.01 =
(c)
log16 4 =
Simplifying Logarithmic and
Exponential Expressions
Simplifying Logarithmic and
Exponential Expressions
loga y = exponent to which the base a must be
raised to obtain y
Note: loga y = x is equivalent to ax = y
Example 1 Simplify the following expression.
log 3 (34 ) + log 3 (3) =
Simplifying Logarithmic and
Exponential Expressions
loga y = exponent to which the base a must be
raised to obtain y
Note: loga y = x is equivalent to ax = y
Example 2 Simplify the following expressions.
ln (e5 )
(a)
e
(b)
2log2 8 =
=