A logarithm is the inverse operation of exponentiation.
It answers the question: “To what exponent must I raise a base to get a number?”
As you can see, the sentence “a log is a power” can be useful as a small reminder: The base of the log is the base, the inside of the log is the result, the output of the log is the power.
A log function shows the base as a subscript. If no subscript, it is assumed the base is 10 - so .
If then .
To evaluate , we must restrict and .
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To evaluate $\log_a(b)$, we must restrict ==$b\in(0,\infty)$ and $a\in(0,\infty) \backslash \{1\}$.==log identities
1
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==$\log_a(m)+\log_a(n)$== = ==$\log_a(mn)$==2
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==$\log_a(m)-\log_a(n)$== = ==$\log_a(\dfrac{m}{n})$==3
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==$p\cdot \log_a(m)$== = ==$\log_a(m^p)$==the easy ones
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$\log_a(1)$ = ==$0$==change of base
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$\log_a(b)$ = ==$\dfrac{\log_{c}(b)}{\log_{c}(a)}$==special case of the change of base
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==$\log_a(b)$== = $\dfrac{1}{\log_b(a)}$