Algebra Examples

\log_{2} (7)

$\log_{2} (7)$

Step 1

The change of base rule can be used if

a

$a$ and

b

$b$ are greater than

0

$0$ and not equal to

1

$1$ , and

x

$x$ is greater than

0

$0$ .

\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 2

Substitute in values for the variables in the change of base formula, using

b = 10

$b = 10$ .

\frac{\log (7)}{\log (2)}

$\frac{\log (7)}{\log (2)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{\log (7)}{\log (2)}

$\frac{\log (7)}{\log (2)}$

Decimal Form:

2.80735492 \dots

$2.80735492 \dots$

\log_{2} 7

$\log_{2} 7$

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