Solve for x 3^(x-4)<1/27

$3^{x - 4} < \frac{1}{27}$

Step 1

Raise $27$ to the power of $1$ .

$3^{x - 4} < \frac{1}{27^{1}}$

Step 2

Move $27^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{x - 4} < 27^{- 1}$

Step 3

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

$3^{x - 4} < 3^{- 3}$

Step 4

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

$x - 4 < - 3$

Step 5

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

Add $4$ to both sides of the inequality.

$x < - 3 + 4$

Add $- 3$ and $4$ .

$x < 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 1$

Interval Notation:

$(- \infty, 1)$

Step 7