Solve for x (3x/2)(3x/4)=3^6

$(3 \frac{x}{2}) (3 \frac{x}{4}) = 3^{6}$

Step 1

Simplify.

Combine $3$ and $\frac{x}{2}$ .

$\frac{3 x}{2} \cdot (3 (\frac{x}{4})) = 3^{6}$

Combine $3$ and $\frac{x}{4}$ .

$\frac{3 x}{2} \cdot \frac{3 x}{4} = 3^{6}$

Multiply $\frac{3 x}{2}$ by $\frac{3 x}{4}$ .

$\frac{3 x (3 x)}{2 \cdot 4} = 3^{6}$

Multiply $3$ by $3$ .

$\frac{9 x \cdot x}{2 \cdot 4} = 3^{6}$

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

$\frac{9 (x^{1} x)}{2 \cdot 4} = 3^{6}$

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

$\frac{9 (x^{1} x^{1})}{2 \cdot 4} = 3^{6}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 x^{1 + 1}}{2 \cdot 4} = 3^{6}$

Add $1$ and $1$ .

$\frac{9 x^{2}}{2 \cdot 4} = 3^{6}$

Multiply $2$ by $4$ .

$\frac{9 x^{2}}{8} = 3^{6}$

Step 2

Divide each term in $\frac{9 x^{2}}{8} = 3^{6}$ by $9$ and simplify.

Divide each term in $\frac{9 x^{2}}{8} = 3^{6}$ by $9$ .

$\frac{\frac{9 x^{2}}{8}}{9} = \frac{3^{6}}{9}$

Simplify the left side.

Multiply the numerator by the reciprocal of the denominator.

$\frac{9 x^{2}}{8} \cdot \frac{1}{9} = \frac{3^{6}}{9}$

Combine.

$\frac{9 x^{2} \cdot 1}{8 \cdot 9} = \frac{3^{6}}{9}$

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2} \cdot 1}{8 \cdot 9} = \frac{3^{6}}{9}$

Rewrite the expression.

$\frac{x^{2} \cdot 1}{8} = \frac{3^{6}}{9}$

Multiply $x^{2}$ by $1$ .

$\frac{x^{2}}{8} = \frac{3^{6}}{9}$

Simplify the right side.

Raise $3$ to the power of $6$ .

$\frac{x^{2}}{8} = \frac{729}{9}$

Divide $729$ by $9$ .

$\frac{x^{2}}{8} = 81$

Step 3

Multiply both sides of the equation by $8$ .

$8 \frac{x^{2}}{8} = 8 \cdot 81$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{x^{2}}{8} = 8 \cdot 81$

Rewrite the expression.

$x^{2} = 8 \cdot 81$

Simplify the right side.

Multiply $8$ by $81$ .

$x^{2} = 648$

Step 5

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{648}$

Step 6

Simplify $\pm \sqrt{648}$ .

Rewrite $648$ as $18^{2} \cdot 2$ .

Factor $324$ out of $648$ .

$x = \pm \sqrt{324 (2)}$

Rewrite $324$ as $18^{2}$ .

$x = \pm \sqrt{18^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm 18 \sqrt{2}$

Step 7

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 18 \sqrt{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 18 \sqrt{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 18 \sqrt{2}, - 18 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 18 \sqrt{2}, - 18 \sqrt{2}$

Decimal Form:

$x = 25.45584412 \dots, - 25.45584412 \dots$

Solve for x (3x/2)(3x/4)=3^6

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