Solve for x log base x of 8=-1

$\log_{x} (8) = - 1$

Rewrite $\log_{x} (8) = - 1$ 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 $b^{y} = x$ .

$x^{- 1} = 8$

Solve for $x$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x} = 8$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Multiply each term in $\frac{1}{x} = 8$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{1}{x} = 8$ by $x$ .

$\frac{1}{x} x = 8 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{1}{x} x = 8 x$

Rewrite the expression.

$1 = 8 x$

Solve the equation.

Rewrite the equation as $8 x = 1$ .

$8 x = 1$

Divide each term in $8 x = 1$ by $8$ and simplify.

Divide each term in $8 x = 1$ by $8$ .

$\frac{8 x}{8} = \frac{1}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{1}{8}$

Divide $x$ by $1$ .

$x = \frac{1}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{8}$

Decimal Form:

$x = 0.125$

Solve for x log base x of 8=-1

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