Solve for x 12^(x-4)>144^(x-6)

$12^{x - 4} > 144^{x - 6}$

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

$12^{x - 4} > 12^{2 (x - 6)}$

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

$x - 4 > 2 (x - 6)$

Solve for $x$ .

Simplify $2 (x - 6)$ .

Rewrite.

$x - 4 > 0 + 0 + 2 (x - 6)$

Simplify by adding zeros.

$x - 4 > 2 (x - 6)$

Apply the distributive property.

$x - 4 > 2 x + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$x - 4 > 2 x - 12$

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

Subtract $2 x$ from both sides of the inequality.

$x - 4 - 2 x > - 12$

Subtract $2 x$ from $x$ .

$- x - 4 > - 12$

Move all terms not containing $x$ to the right side of the inequality.

Add $4$ to both sides of the inequality.

$- x > - 12 + 4$

Add $- 12$ and $4$ .

$- x > - 8$

Divide each term in $- x > - 8$ by $- 1$ and simplify.

Divide each term in $- x > - 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{- 8}{- 1}$

Divide $x$ by $1$ .

$x < \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$x < 8$

The result can be shown in multiple forms.

Inequality Form:

$x < 8$

Interval Notation:

$(- \infty, 8)$

Solve for x 12^(x-4)>144^(x-6)

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