Algebra Examples

$\log (5 (x + 6)) = \log (8 (9 x))$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$5 (x + 6) = 8 \cdot (9 x)$

Step 2

Solve for $x$ .

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Step 2.1

Simplify $5 (x + 6)$ .

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Step 2.1.1

Rewrite.

$0 + 0 + 5 (x + 6) = 8 \cdot (9 x)$

Step 2.1.2

Simplify by adding zeros.

$5 (x + 6) = 8 \cdot (9 x)$

Step 2.1.3

Apply the distributive property.

$5 x + 5 \cdot 6 = 8 \cdot (9 x)$

Step 2.1.4

Multiply $5$ by $6$ .

$5 x + 30 = 8 \cdot (9 x)$

Step 2.2

Multiply $9$ by $8$ .

$5 x + 30 = 72 x$

Step 2.3

Move all terms containing $x$ to the left side of the equation.

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Step 2.3.1

Subtract $72 x$ from both sides of the equation.

$5 x + 30 - 72 x = 0$

Step 2.3.2

Subtract $72 x$ from $5 x$ .

$- 67 x + 30 = 0$

Step 2.4

Subtract $30$ from both sides of the equation.

$- 67 x = - 30$

Step 2.5

Divide each term in $- 67 x = - 30$ by $- 67$ and simplify.

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Step 2.5.1

Divide each term in $- 67 x = - 30$ by $- 67$ .

$\frac{- 67 x}{- 67} = \frac{- 30}{- 67}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $- 67$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{- 67 x}{- 67} = \frac{- 30}{- 67}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 30}{- 67}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Dividing two negative values results in a positive value.

$x = \frac{30}{67}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{30}{67}$

Decimal Form:

$x = 0.44776119 \dots$