Basic Math Examples

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

Step 1

Rewrite $\log_{b} (1) = 0$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$b^{0} = 1$

Step 2

Solve for $b$ .

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Step 2.1

Anything raised to $0$ is $1$ .

$1 = 1$

Step 2.2

Since $1 = 1$ , the equation will always be true for any value of $b$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$