Solve for t log of 2t+4 = log of 14-3t

$\log (2 t + 4) = \log (14 - 3 t)$

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

$2 t + 4 = 14 - 3 t$

Solve for $t$ .

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

Add $3 t$ to both sides of the equation.

$2 t + 4 + 3 t = 14$

Add $2 t$ and $3 t$ .

$5 t + 4 = 14$

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

Subtract $4$ from both sides of the equation.

$5 t = 14 - 4$

Subtract $4$ from $14$ .

$5 t = 10$

Divide each term in $5 t = 10$ by $5$ and simplify.

Divide each term in $5 t = 10$ by $5$ .

$\frac{5 t}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 t}{5} = \frac{10}{5}$

Divide $t$ by $1$ .

$t = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$t = 2$