Solve for x 27^(4x-1)=9^(3x+8)

$27^{4 x - 1} = 9^{3 x + 8}$

Step 1

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

$3^{3 (4 x - 1)} = 3^{2 (3 x + 8)}$

Step 2

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

$3 (4 x - 1) = 2 (3 x + 8)$

Step 3

Solve for $x$ .

Simplify $3 (4 x - 1)$ .

Rewrite.

$0 + 0 + 3 (4 x - 1) = 2 (3 x + 8)$

Simplify by adding zeros.

$3 (4 x - 1) = 2 (3 x + 8)$

Apply the distributive property.

$3 (4 x) + 3 \cdot - 1 = 2 (3 x + 8)$

Multiply.

Multiply $4$ by $3$ .

$12 x + 3 \cdot - 1 = 2 (3 x + 8)$

Multiply $3$ by $- 1$ .

$12 x - 3 = 2 (3 x + 8)$

Simplify $2 (3 x + 8)$ .

Apply the distributive property.

$12 x - 3 = 2 (3 x) + 2 \cdot 8$

Multiply.

Multiply $3$ by $2$ .

$12 x - 3 = 6 x + 2 \cdot 8$

Multiply $2$ by $8$ .

$12 x - 3 = 6 x + 16$

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

Subtract $6 x$ from both sides of the equation.

$12 x - 3 - 6 x = 16$

Subtract $6 x$ from $12 x$ .

$6 x - 3 = 16$

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

Add $3$ to both sides of the equation.

$6 x = 16 + 3$

Add $16$ and $3$ .

$6 x = 19$

Divide each term in $6 x = 19$ by $6$ and simplify.

Divide each term in $6 x = 19$ by $6$ .

$\frac{6 x}{6} = \frac{19}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{19}{6}$

Divide $x$ by $1$ .

$x = \frac{19}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{6}$

Decimal Form:

$x = 3.1\overline{6}$

Mixed Number Form:

$x = 3 \frac{1}{6}$

Solve for x 27^(4x-1)=9^(3x+8)

Related Questions

Support LCMGCF.com by disabling your adblocker.