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"Log" is short for Logarithm and can be to any base.
The Logarithm of a number is the number to which the base has to be raised to get that number; that is why there are no logarithms for negative numbers. For example: 10² = 100 → log to base 10 of 100 is 2.
There are two specific abbreviations:
- lg is the log to base 10
- ln is the log to base e - e is Euler's number and is approximately 2.71828184; logs to base e are known as natural logs.
On an electronic calculator the [log] button takes logarithms to base 10. The inverse function (anti-log) is marked as 10^x.
Similarly the [ln] button takes logs to base e, with the inverse function marked as e^x.
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Write this in the form of single logarithm log x plus log y?
That is the same as log xy.
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2*log(15) = log(x) 152 = x; its equivalent logarithmic form is 2 = log15 x (exponents are logarithms) then, it is equivalent to 2log 15 = log x, equivalent to log 152 = log x (the power rule), ... 2 = log15 x 2 = log x/log 15 (using the change-base property) 2log 15 = log x Thus, we can say that 152 = x is equivalent to 2*log(15) = log(x) (equivalents to equivalents are equivalent)
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That is the same as log xy.
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