Solve for y 81^y<27^(y+3)

$81^{y} < 27^{y + 3}$

Step 1

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

$3^{4 y} < 3^{3 (y + 3)}$

Step 2

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

$4 y < 3 (y + 3)$

Step 3

Solve for $y$ .

Simplify $3 (y + 3)$ .

Apply the distributive property.

$4 y < 3 y + 3 \cdot 3$

Multiply $3$ by $3$ .

$4 y < 3 y + 9$

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

Subtract $3 y$ from both sides of the inequality.

$4 y - 3 y < 9$

Subtract $3 y$ from $4 y$ .

$y < 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < 9$

Interval Notation:

$(- \infty, 9)$

Step 5