Algebra Examples

$\log (9) (x + 4) = \log (2) (6 x)$

Step 1

Simplify the expressions in the equation.

Tap for more steps...

Step 1.1

Simplify the left side.

Tap for more steps...

Step 1.1.1

Simplify $\log (9) (x + 4)$ .

Tap for more steps...

Step 1.1.1.1

Apply the distributive property.

$\log (9) x + \log (9) \cdot 4 = \log (2) \cdot (6 x)$

Step 1.1.1.2

Move $4$ to the left of $\log (9)$ .

$\log (9) x + 4 \log (9) = \log (2) \cdot (6 x)$

Step 1.2

Simplify the right side.

Tap for more steps...

Step 1.2.1

Rewrite using the commutative property of multiplication.

$\log (9) x + 4 \log (9) = 6 \log (2) x$

Step 2

Move all the terms containing a logarithm to the left side of the equation.

$\log (9) x + 4 \log (9) - 6 \log (2) x = 0$

Step 3

Reorder factors in $\log (9) x + 4 \log (9) - 6 \log (2) x$ .

$x \log (9) + 4 \log (9) - 6 x \log (2) = 0$

Step 4

Simplify the left side.

Tap for more steps...

Step 4.1

Simplify $x \log (9) + 4 \log (9) - 6 x \log (2)$ .

Tap for more steps...

Step 4.1.1

Simplify each term.

Tap for more steps...

Step 4.1.1.1

Simplify $4 \log (9)$ by moving $4$ inside the logarithm.

$x \log (9) + \log (9^{4}) - 6 x \log (2) = 0$

Step 4.1.1.2

Raise $9$ to the power of $4$ .

$x \log (9) + \log (6561) - 6 x \log (2) = 0$

Step 4.1.1.3

Simplify $- 6 \log (2)$ by moving $6$ inside the logarithm.

$x \log (9) + \log (6561) + x (- \log (2^{6})) = 0$

Step 4.1.1.4

Raise $2$ to the power of $6$ .

$x \log (9) + \log (6561) + x (- \log (64)) = 0$

Step 4.1.2

Reorder factors in $x \log (9) + \log (6561) + x (- \log (64))$ .

$x \log (9) + \log (6561) - x \log (64) = 0$

Step 5

Subtract $\log (6561)$ from both sides of the equation.

$x \log (9) - x \log (64) = - \log (6561)$

Step 6

Factor $x$ out of $x \log (9) - x \log (64)$ .

Tap for more steps...

Step 6.1

Factor $x$ out of $x \log (9)$ .

$x (\log (9)) - x \log (64) = - \log (6561)$

Step 6.2

Factor $x$ out of $- x \log (64)$ .

$x (\log (9)) + x (- 1 \log (64)) = - \log (6561)$

Step 6.3

Factor $x$ out of $x (\log (9)) + x (- 1 \log (64))$ .

$x (\log (9) - 1 \log (64)) = - \log (6561)$

Step 7

Rewrite $- 1 \log (64)$ as $- \log (64)$ .

$x (\log (9) - \log (64)) = - \log (6561)$

Step 8

Divide each term in $x (\log (9) - \log (64)) = - \log (6561)$ by $\log (9) - \log (64)$ and simplify.

Tap for more steps...

Step 8.1

Divide each term in $x (\log (9) - \log (64)) = - \log (6561)$ by $\log (9) - \log (64)$ .

$\frac{x (\log (9) - \log (64))}{\log (9) - \log (64)} = \frac{- \log (6561)}{\log (9) - \log (64)}$

Step 8.2

Simplify the left side.

Tap for more steps...

Step 8.2.1

Cancel the common factor of $\log (9) - \log (64)$ .

Tap for more steps...

Step 8.2.1.1

Cancel the common factor.

$\frac{x (\log (9) - \log (64))}{\log (9) - \log (64)} = \frac{- \log (6561)}{\log (9) - \log (64)}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \log (6561)}{\log (9) - \log (64)}$

Step 8.3

Simplify the right side.

Tap for more steps...

Step 8.3.1

Move the negative in front of the fraction.

$x = - \frac{\log (6561)}{\log (9) - \log (64)}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\log (6561)}{\log (9) - \log (64)}$

Decimal Form:

$x = 4.48034063 \dots$