Solve for x log base 5 of 5x+9 = log base 5 of 6x

$\log_{5} (5 x + 9) = \log_{5} (6 x)$

Step 1

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

$5 x + 9 = 6 x$

Step 2

Solve for $x$ .

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

Subtract $6 x$ from both sides of the equation.

$5 x + 9 - 6 x = 0$

Subtract $6 x$ from $5 x$ .

$- x + 9 = 0$

Subtract $9$ from both sides of the equation.

$- x = - 9$

Divide each term in $- x = - 9$ by $- 1$ and simplify.

Divide each term in $- x = - 9$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 9}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$x = 9$