Solve for x 3^(4-3x)>(1/243)

$3^{4 - 3 x} > (\frac{1}{243})$

Step 1

Raise $243$ to the power of $1$ .

$3^{4 - 3 x} > \frac{1}{243^{1}}$

Step 2

Move $243^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{4 - 3 x} > 243^{- 1}$

Step 3

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

$3^{4 - 3 x} > 3^{- 5}$

Step 4

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

$4 - 3 x > - 5$

Step 5

Solve for $x$ .

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

Subtract $4$ from both sides of the inequality.

$- 3 x > - 5 - 4$

Subtract $4$ from $- 5$ .

$- 3 x > - 9$

Divide each term in $- 3 x > - 9$ by $- 3$ and simplify.

Divide each term in $- 3 x > - 9$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{- 9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{- 9}{- 3}$

Divide $x$ by $1$ .

$x < \frac{- 9}{- 3}$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 3$

Interval Notation:

$(- \infty, 3)$

Step 7

Solve for x 3^(4-3x)>(1/243)

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