Why is $\log_6 1$ equal to $0$ ?
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Where is the user guide for math matrix – user161304 Jul 09 '14 at 16:25
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Remember that $\log_a b = x$ is really just $a^x = b$ in disguise. Therefore, you have
$$6^x = 1$$
So basically, what values of $x$ will make the answer $1$? Well, it's gotta be $0$.
So from this you can deduce that any which looks like
$$\log_x 1$$
must have the answer zero or in other words,
$$\log_x 1 = 0$$
Jeel Shah
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Because $6^0=1$. Simple as that. In fact, $\log_a 1=0$ for any value of $a>0$.
The $\log$ function is the inverse function to the exponential function. Thus, the number $x=\log_a b$ is the number that solves the equation $a^x = b$.
Apply this to your example: what is $x=\log_6 1$? To what power must you put $6$ to get $1$? Well, you know that $6^0 = 1$, right? this means that by definition, $0 = \log_6 1$.
5xum
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Right a^0=1 any number to the zero power equals 1 got you thanks. I know it was simple. – user161304 Jul 09 '14 at 16:07
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$\log_b (xy) = \log_b x + \log_b y$. Since $1x = x$, we must have $\log_b 1 = 0$.
martini
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copper.hat
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$$\log_6\frac11=\log_61-\log_61.$$