Precalculus Examples

${(\frac{9}{16})}^{3 x - 2} = {(\frac{3}{4})}^{5 x + 4}$

Step 1

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

${(\frac{3}{4})}^{2 (3 x - 2)} = {(\frac{3}{4})}^{5 x + 4}$

Step 2

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

$2 (3 x - 2) = 5 x + 4$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Simplify $2 (3 x - 2)$ .

Tap for more steps...

Step 3.1.1

Rewrite.

$0 + 0 + 2 (3 x - 2) = 5 x + 4$

Step 3.1.2

Simplify by adding zeros.

$2 (3 x - 2) = 5 x + 4$

Step 3.1.3

Apply the distributive property.

$2 (3 x) + 2 \cdot - 2 = 5 x + 4$

Step 3.1.4

Multiply.

Tap for more steps...

Step 3.1.4.1

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 2 = 5 x + 4$

Step 3.1.4.2

Multiply $2$ by $- 2$ .

$6 x - 4 = 5 x + 4$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$6 x - 4 - 5 x = 4$

Step 3.2.2

Subtract $5 x$ from $6 x$ .

$x - 4 = 4$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Add $4$ to both sides of the equation.

$x = 4 + 4$

Step 3.3.2

Add $4$ and $4$ .

$x = 8$