Solve for k log of 4k-5 = log of 2k-1

$\log (4 k - 5) = \log (2 k - 1)$

Step 1

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

$4 k - 5 = 2 k - 1$

Step 2

Solve for $k$ .

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

Subtract $2 k$ from both sides of the equation.

$4 k - 5 - 2 k = - 1$

Subtract $2 k$ from $4 k$ .

$2 k - 5 = - 1$

Move all terms not containing $k$ to the right side of the equation.

Add $5$ to both sides of the equation.

$2 k = - 1 + 5$

Add $- 1$ and $5$ .

$2 k = 4$

Divide each term in $2 k = 4$ by $2$ and simplify.

Divide each term in $2 k = 4$ by $2$ .

$\frac{2 k}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 k}{2} = \frac{4}{2}$

Divide $k$ by $1$ .

$k = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$k = 2$