Linear Algebra Examples

$\log_{x} (y) = 6$

Step 1

Rewrite $\log_{x} (y) = 6$ 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 $b^{y} = x$ .

$x^{6} = y$

Step 2

Rewrite the equation as $y = x^{6}$ .

$y = x^{6}$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4