Solve for x 3^(x-10)<=3^(5x-38)

$3^{x - 10} \leq 3^{5 x - 38}$

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

$3^{x - 10} \leq 3^{5 x - 38}$

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

$x - 10 \leq 5 x - 38$

Solve for $x$ .

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

Subtract $5 x$ from both sides of the inequality.

$x - 10 - 5 x \leq - 38$

Subtract $5 x$ from $x$ .

$- 4 x - 10 \leq - 38$

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

Add $10$ to both sides of the inequality.

$- 4 x \leq - 38 + 10$

Add $- 38$ and $10$ .

$- 4 x \leq - 28$

Divide each term in $- 4 x \leq - 28$ by $- 4$ and simplify.

Divide each term in $- 4 x \leq - 28$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \geq \frac{- 28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \geq \frac{- 28}{- 4}$

Divide $x$ by $1$ .

$x \geq \frac{- 28}{- 4}$

Simplify the right side.

Divide $- 28$ by $- 4$ .

$x \geq 7$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 7$

Interval Notation:

$[7, \infty)$

Solve for x 3^(x-10)<=3^(5x-38)

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