Solve for x log of 6(x+3) = log of 7(8x)

$\log (6 (x + 3)) = \log (7 (8 x))$

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

$6 (x + 3) = 7 \cdot (8 x)$

Solve for $x$ .

Simplify $6 (x + 3)$ .

Start simplifying.

$0 + 0 + 6 (x + 3) = 7 \cdot (8 x)$

Simplify by adding zeros.

$6 (x + 3) = 7 \cdot (8 x)$

Apply the distributive property.

$6 x + 6 \cdot 3 = 7 \cdot (8 x)$

Multiply $6$ by $3$ .

$6 x + 18 = 7 \cdot (8 x)$

Multiply $8$ by $7$ .

$6 x + 18 = 56 x$

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

Subtract $56 x$ from both sides of the equation.

$6 x + 18 - 56 x = 0$

Subtract $56 x$ from $6 x$ .

$- 50 x + 18 = 0$

Subtract $18$ from both sides of the equation.

$- 50 x = - 18$

Divide each term in $- 50 x = - 18$ by $- 50$ and simplify.

Divide each term in $- 50 x = - 18$ by $- 50$ .

$\frac{- 50 x}{- 50} = \frac{- 18}{- 50}$

Simplify the left side.

Cancel the common factor of $- 50$ .

Cancel the common factor.

$\frac{- 50 x}{- 50} = \frac{- 18}{- 50}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 50}$

Simplify the right side.

Cancel the common factor of $- 18$ and $- 50$ .

Factor $- 2$ out of $- 18$ .

$x = \frac{- 2 (9)}{- 50}$

Cancel the common factors.

Factor $- 2$ out of $- 50$ .

$x = \frac{- 2 \cdot 9}{- 2 \cdot 25}$

Cancel the common factor.

$x = \frac{- 2 \cdot 9}{- 2 \cdot 25}$

Rewrite the expression.

$x = \frac{9}{25}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{25}$

Decimal Form:

$x = 0.36$

Solve for x log of 6(x+3) = log of 7(8x)

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