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Properties of Logarithms
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Properties of logarithms
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Properties of Logarithmic Functions
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Let  ,  , let  and  be positive numbers, and let  be any real number. Then the following properties hold:
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1.
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The range of ](/support/helpjp/helpview.aspx?si=8413/file02314/math52.png) is all real numbers.
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2.
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The domain of ](/support/helpjp/helpview.aspx?si=8413/file02314/math61.png) is all positive real numbers.
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4.
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 = 0](/support/helpjp/helpview.aspx?si=8413/file02314/math85.png)
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5.
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 = log[b](x)+log[b](y)](/support/helpjp/helpview.aspx?si=8413/file02314/math90.png)
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6.
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 = log[b](x)-log[b](y)](/support/helpjp/helpview.aspx?si=8413/file02314/math95.png)
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7.
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 = -log[b](x)](/support/helpjp/helpview.aspx?si=8413/file02314/math100.png)
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8.
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 = r*log[b](x)](/support/helpjp/helpview.aspx?si=8413/file02314/math105.png)
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Using the properties of logarithms
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The calculator shown here is missing a few keys (no multiplication or division keys). Nonetheless, it is still possible to perform any arithmetic calculation involving only +, -, ×, or ÷ operations. This is because the calculator has "10 to the power of" and "logarithm base 10" keys.
Try it out. Can you compute these values?
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The "log" button represents the base 10 logarithmic function. The calculator displays answers to 2 decimal places.
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