Solve for x log base 27 of 3=x

$\log_{27} (3) = x$

Rewrite the equation as $x = \log_{27} (3)$ .

$x = \log_{27} (3)$

Logarithm base $27$ of $3$ is $\frac{1}{3}$ .

Rewrite as an equation.

$x = \log_{27} (3) = x$

Rewrite $\log_{27} (3) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$x = 27^{x} = 3$

Create expressions in the equation that all have equal bases.

$x = {(3^{3})}^{x} = 3^{1}$

Rewrite ${(3^{3})}^{x}$ as $3^{3 x}$ .

$x = 3^{3 x} = 3^{1}$

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

$x = 3 x = 1$

Solve for $x$ .

$x = x = \frac{1}{3}$

The variable $x$ is equal to $\frac{1}{3}$ .

$x = \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$

Solve for x log base 27 of 3=x

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