Solve the Inequality for m 2^(3m-4)>4

$2^{3 m - 4} > 4$

Step 1

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

$2^{3 m - 4} > 2^{2}$

Step 2

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

$3 m - 4 > 2$

Step 3

Solve for $m$ .

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

Add $4$ to both sides of the inequality.

$3 m > 2 + 4$

Add $2$ and $4$ .

$3 m > 6$

Divide each term in $3 m > 6$ by $3$ and simplify.

Divide each term in $3 m > 6$ by $3$ .

$\frac{3 m}{3} > \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 m}{3} > \frac{6}{3}$

Divide $m$ by $1$ .

$m > \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$m > 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m > 2$

Interval Notation:

$(2, \infty)$

Step 5