Solve for x 9^(15x-48)=3^(3x^2-6x)

$9^{15 x - 48} = 3^{3 x^{2} - 6 x}$

Create equivalent expressions in the equation that all have equal bases.

$3^{2 (15 x - 48)} = 3^{3 x^{2} - 6 x}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 (15 x - 48) = 3 x^{2} - 6 x$

Solve for $x$ .

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 x^{2} - 6 x = 2 (15 x - 48)$

Simplify $2 (15 x - 48)$ .

Apply the distributive property.

$3 x^{2} - 6 x = 2 (15 x) + 2 \cdot - 48$

Multiply.

Multiply $15$ by $2$ .

$3 x^{2} - 6 x = 30 x + 2 \cdot - 48$

Multiply $2$ by $- 48$ .

$3 x^{2} - 6 x = 30 x - 96$

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

Subtract $30 x$ from both sides of the equation.

$3 x^{2} - 6 x - 30 x = - 96$

Subtract $30 x$ from $- 6 x$ .

$3 x^{2} - 36 x = - 96$

Add $96$ to both sides of the equation.

$3 x^{2} - 36 x + 96 = 0$

Factor the left side of the equation.

Factor $3$ out of $3 x^{2} - 36 x + 96$ .

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) - 36 x + 96 = 0$

Factor $3$ out of $- 36 x$ .

$3 (x^{2}) + 3 (- 12 x) + 96 = 0$

Factor $3$ out of $96$ .

$3 x^{2} + 3 (- 12 x) + 3 \cdot 32 = 0$

Factor $3$ out of $3 x^{2} + 3 (- 12 x)$ .

$3 (x^{2} - 12 x) + 3 \cdot 32 = 0$

Factor $3$ out of $3 (x^{2} - 12 x) + 3 \cdot 32$ .

$3 (x^{2} - 12 x + 32) = 0$

Factor.

Factor $x^{2} - 12 x + 32$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $32$ and whose sum is $- 12$ .

$- 8, - 4$

Write the factored form using these integers.

$3 ((x - 8) (x - 4)) = 0$

Remove unnecessary parentheses.

$3 (x - 8) (x - 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 8 = 0$

$x - 4 = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $3 (x - 8) (x - 4) = 0$ true.

$x = 8, 4$

Solve for x 9^(15x-48)=3^(3x^2-6x)

Related Questions

Support LCMGCF.com by disabling your adblocker.