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I am reading this page about logarithm: http://www.andrews.edu/~calkins/math/webtexts/numb17.htm

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!

2 Answers 2

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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.

1

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.

See http://en.wikipedia.org/wiki/Exponentiation#Positive_integer_exponents