Solve for x 9^(2x-15)=(1/27)^(4x)

$9^{2 x - 15} = {(\frac{1}{27})}^{4 x}$

Step 1

Apply the product rule to $\frac{1}{27}$ .

$9^{2 x - 15} = \frac{1^{4 x}}{27^{4 x}}$

Step 2

One to any power is one.

$9^{2 x - 15} = \frac{1}{27^{4 x}}$

Step 3

Move $27^{4 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$9^{2 x - 15} = 27^{- 4 x}$

Step 4

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

$3^{2 (2 x - 15)} = 3^{3 (- 4 x)}$

Step 5

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

$2 (2 x - 15) = 3 (- 4 x)$

Step 6

Solve for $x$ .

Simplify $2 (2 x - 15)$ .

Start simplifying.

$0 + 0 + 2 (2 x - 15) = 3 (- 4 x)$

Simplify by adding zeros.

$2 (2 x - 15) = 3 (- 4 x)$

Apply the distributive property.

$2 (2 x) + 2 \cdot - 15 = 3 (- 4 x)$

Multiply.

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 15 = 3 (- 4 x)$

Multiply $2$ by $- 15$ .

$4 x - 30 = 3 (- 4 x)$

Multiply $- 4$ by $3$ .

$4 x - 30 = - 12 x$

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

Add $12 x$ to both sides of the equation.

$4 x - 30 + 12 x = 0$

Add $4 x$ and $12 x$ .

$16 x - 30 = 0$

Add $30$ to both sides of the equation.

$16 x = 30$

Divide each term in $16 x = 30$ by $16$ and simplify.

Divide each term in $16 x = 30$ by $16$ .

$\frac{16 x}{16} = \frac{30}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{30}{16}$

Divide $x$ by $1$ .

$x = \frac{30}{16}$

Simplify the right side.

Cancel the common factor of $30$ and $16$ .

Factor $2$ out of $30$ .

$x = \frac{2 (15)}{16}$

Cancel the common factors.

Factor $2$ out of $16$ .

$x = \frac{2 \cdot 15}{2 \cdot 8}$

Cancel the common factor.

$x = \frac{2 \cdot 15}{2 \cdot 8}$

Rewrite the expression.

$x = \frac{15}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{8}$

Decimal Form:

$x = 1.875$

Mixed Number Form:

$x = 1 \frac{7}{8}$

Solve for x 9^(2x-15)=(1/27)^(4x)

Related Questions

Support LCMGCF.com by disabling your adblocker.