$\log_{b}{1} \,=\, 0$

The logarithm of one should be evaluated often with different bases in mathematics. So, it is essential for everyone to know the exact value of the logarithm of one at the beginning level of studying the logarithms. Actually, the logarithm of one to any base quantity is equal to zero and this property is called the logarithm of one rule.

Look at the following examples.

$(1).\,\,$ $\log_{5}{(1)} \,=\, 0$

$(2).\,\,$ $\log_{12}{(1)} \,=\, 0$

$(3).\,\,$ $\log_{617}{(1)} \,=\, 0$

You can understand that the value of the logarithm of one to any base number is zero. Hence, the base of the logarithm is denoted by an algebraic literal $b$ and the logarithm of one law can be expressed in algebraic form as follows.

$\therefore \,\,\,\,$ $\log_{b}{(1)} \,=\, 0$

Learn how to prove the logarithm of one property in algebraic form for using it as a formula in mathematics.

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