Algebra Examples

$\log (6 x) - 3 = - 4$

Step 1

Move all terms not containing $\log (6 x)$ to the right side of the equation.

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Step 1.1

Add $3$ to both sides of the equation.

$\log (6 x) = - 4 + 3$

Step 1.2

Add $- 4$ and $3$ .

$\log (6 x) = - 1$

Step 2

Rewrite $\log (6 x) = - 1$ 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 $b^{y} = x$ .

$10^{- 1} = 6 x$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $6 x = 10^{- 1}$ .

$6 x = 10^{- 1}$

Step 3.2

Divide each term in $6 x = 10^{- 1}$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 x = 10^{- 1}$ by $6$ .

$\frac{6 x}{6} = \frac{10^{- 1}}{6}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{10^{- 1}}{6}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10^{- 1}}{6}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move $10^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x = \frac{1}{6 \cdot 10}$

Step 3.2.3.2

Multiply $6$ by $10$ .

$x = \frac{1}{60}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{60}$

Decimal Form:

$x = 0.01\overline{6}$