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Introduction When ax=y, in order to solve for x in terms of y, x cannot be expressed as a polynomial function, a fractional function, a root function or a compound function of these functions. (None of the functions that you have learned in the previous lessons.) So we will define a new function called ”logarithm” denoted by log. Definition of Logarithm
When a>0 and a≠1
 Base =Not change= Base Argument ←Change→ Value
The exponential function y=ax is defined if a>0 and a≠1. So, when we define the inverse of the exponential function, we suppose a>0 and a≠1.
• Each of the following expressions has the same meaning.• The base in the logarithmic expression is the same with the base in the exponential expression. |
If you cannot understand what the logarithm expresses, convert it to exponential form. 3=log28 means 23=8 2=log39 means 32=9 4=log1010000 means 104=10000 0=log51 means 50=1 Example 1Convert the following expressions into the exponential expressions.
(1)4=log216
(Answer)24=16 If you write 42=16, the expression itself is true but it doesn’t correspond to the logarithmic expressions.(The base is not the same.)
(2)log101000=3
(Answer)103=1000
(3)log5 =−2
(Answer)5−2= Example 2Convert the following expressions into the logarithmic expressions.
(1)42=16
(Answer)log416=2
(2)8=4
(Answer)log84=
(3)10−2=0.01
(Answer)log100.01=−2 |
Question 1Convert the following expressions into the exponential expressions.
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9=2
9=23
2−3=
9−= 9=3 9=32 3−2= 9−= |
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9=2
9=23
2−3=
9−= 9=3 9=32 3−2= 9−= |
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9=2
9=23
2−3=
9−= 9=3 9=32 3−2= 9−= |
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8=2
8=23
2−3=
8−= 8=3 8=32 3−2= 8−= |
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8=2
8=23
2−3=
8−= 8=3 8=32 3−2= 8−= |
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8=2
8=23
2−3=
8−= 8=3 8=32 3−2= 8−= |