Algebra Examples

\log_{3} (81) = x

$\log_{3} (81) = x$

Step 1

Rewrite the equation as

x = \log_{3} (81)

$x = \log_{3} (81)$ .

x = \log_{3} (81)

$x = \log_{3} (81)$

Step 2

Logarithm base

3

$3$ of

81

$81$ is

4

$4$ .

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Step 2.1

Rewrite as an equation.

x = \log_{3} (81) = x

$x = \log_{3} (81) = x$

Step 2.2

Rewrite

\log_{3} (81) = x

$\log_{3} (81) = x$ in exponential form using the definition of a logarithm. If

x

$x$ and

b

$b$ are positive real numbers and

b

$b$ does not equal

1

$1$ , then

\log_{b} (x) = y

$\log_{b} (x) = y$ is equivalent to

b^{y} = x

$b^{y} = x$ .

x = 3^{x} = 81

$x = 3^{x} = 81$

Step 2.3

Create equivalent expressions in the equation that all have equal bases.

x = 3^{x} = 3^{4}

$x = 3^{x} = 3^{4}$

Step 2.4

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

x = x = 4

$x = x = 4$

Step 2.5

The variable

x

$x$ is equal to

4

$4$ .

x = 4

$x = 4$

x = 4

$x = 4$