This lesson will show how to evaluate logarithms with three good examples. Study them carefully.
Example #1:
Evaluate log_{8} 16
Write an equation in logarithmic form
log_{8} 16 = x
Convert to exponential form
16 = 8^{x}
Write each side using base 2.
2^{4} = (2^{3})^{x}
2^{4} = 2^{3}^{x}
Since the base or 2 is the same, 2^{4} = 2^{3}^{x} if 4 is equal to 3x
If 4 = 3x, then x = 4/3
Therefore, log_{8} 16 = x = 4/3
Example #2:
Evaluate log_{10} 1000
Write an equation in logarithmic form
log_{10} 1000 = x
Convert to exponential form
1000 = 10^{x}
Write each side using base 10.
10^{3} = (10)^{x}
Since the base or 10 is the same, 10^{3} = 10^{x} if 3 is equal to x
Therefore, log_{10} 1000 = x = 3
Example #3:
Evaluate log_{64} 1/16
Write an equation in logarithmic form
log_{64} 1/16 = x
Convert to exponential form
1/16 = 64^{x}
Write each side using base 4.
1/4^{2} = (4^{3})^{x}
4^{-2} = 4^{3}^{x}
Since the base or 4 is the same, 4^{-2} = 4^{3}^{x} if -2 is equal to 3x
If -2 = 3x, then x = -2/3
Therefore, log_{64} 1/16 = x = -2/3
Feb 17, 19 12:04 PM
There is no rational number whose square is 2. An easy to follow proof by contraction.
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Feb 17, 19 12:04 PM
There is no rational number whose square is 2. An easy to follow proof by contraction.