Converting from Logarithmic to Exponential Form · Example 1 Write the logarithmic equation log 3 (9) = 2 in equivalent exponential form. ( ) ... Example 2 Write the exponential equation
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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
Example 2 Write the logarithmic equation C = log
H (A) in
equivalent exponential form.
= ( )
Converting from Logarithmic to Exponential Form
loga y = x is equivalent to ax = y
Example 3 Write the logarithmic equation log (10,000) = 4 in
equivalent exponential form.
= ( )
Converting from Logarithmic to Exponential Form
Common Logarithm: log10
y = log y
Example 4 Write the logarithmic equation A = ln (19) in
equivalent exponential form.
( ) =
Converting from Logarithmic to Exponential Form
Natural Logarithm: loge y = ln y
(Note: e у�2.718)
Converting from Exponential to Logarithmic Form
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 ( ) =
Converting from Exponential to Logarithmic Form
loga y = x is equivalent to ax = y
Evaluating Logarithms
Example 1 Determine the value of the logarithmic expression.
(a) log2 16 = (b) log 100 = (c) ln e =
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 2 Determine the value of the logarithmic expression.
(a) (b) (c)
Evaluating Logarithms Properties of Exponents:
z0a = 1, a 0 -mm1a =
a§ ·¨ ¸© ¹
-mm1 = a
a
§ ·¨ ¸© ¹
31log =
81
ln 1 =
1/2log 2 =
Example 3 Determine the value of the logarithmic expression.
(a) (b) (c)
Evaluating Logarithms Properties of Exponents:
z0a = 1, a 0 -mm1a =
a§ ·¨ ¸© ¹
-mm1 = a
a1/2a = a
log 0.01 =
6log 6 =
16log 4 =
Simplifying Logarithmic and Exponential Expressions
Example 1 Simplify the following expression.
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
43 3log (3 ) + log (3) =
Example 2 Simplify the following expressions.
(a) (b)
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
2log 82 =
5ln (e )e =
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