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I am reading this page about logarithm:

And saw this piece of transformation:

$$\log_b(\frac{2x^2 + 2x}{12}) = 0$$

Take exponents of both sides, yielding:

$$\frac{x^2 + x}{6}= b^0$$

$$\frac{x^2 + x}{6} = 1$$

I understand where $b^0$ comes from, but could not understand how it became $1$ on the third line.

Can anyone explain?

Much appreciated!

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up vote 1 down vote accepted

b = base which is presumably not infinity.

If you take any base and raise it to zero power, $b^0 = 1$.

Does that make sense?

Note: your formatting has errors.

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For $\log_ba$ to be defined requires base $b$ to be $\gt 0$ and $\neq 1$ and since for any positive real number $b$, $b^0=1$, so it follows.


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