converting from logarithmic to exponential form - mwsu...
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![Page 1: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/1.jpg)
Converting from Logarithmic to Exponential Form
![Page 2: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/2.jpg)
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
![Page 3: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/3.jpg)
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
![Page 4: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/4.jpg)
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
![Page 5: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/5.jpg)
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)
![Page 6: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/6.jpg)
Converting from Exponential to Logarithmic Form
![Page 7: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/7.jpg)
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
![Page 8: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/8.jpg)
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
![Page 9: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/9.jpg)
Evaluating Logarithms
![Page 10: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/10.jpg)
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
![Page 11: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/11.jpg)
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 =
![Page 12: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/12.jpg)
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 =
![Page 13: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/13.jpg)
Simplifying Logarithmic and Exponential Expressions
![Page 14: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/14.jpg)
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) =
![Page 15: Converting from Logarithmic to Exponential Form - MWSU …placement.missouriwestern.edu/pdfs/Tutorial8sheet.pdf · · 2015-03-03Example 1 Write the logarithmic equation log 3 (9)](https://reader034.vdocuments.site/reader034/viewer/2022050814/5ae24df27f8b9a5b348c1412/html5/thumbnails/15.jpg)
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 =