Solve for x log base 3 of 27=x

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Algebra

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

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

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

Logarithm base $3$ of $27$ is $3$ .

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Rewrite as an equation.

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

Rewrite $\log_{3} (27) = x$ 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 $b^{y} = x$ .

$3^{x} = 27$

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

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

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

$x = 3$

The variable $x$ is equal to $3$ .

$x = 3$

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