Solve for x 36^(4x-1)=6^(x+2)

$36^{4 x - 1} = 6^{x + 2}$

Step 1

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

$6^{2 (4 x - 1)} = 6^{x + 2}$

Step 2

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

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

Step 3

Solve for $x$ .

Simplify $2 (4 x - 1)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $4$ by $2$ .

$8 x + 2 \cdot - 1 = x + 2$

Multiply $2$ by $- 1$ .

$8 x - 2 = x + 2$

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

Subtract $x$ from both sides of the equation.

$8 x - 2 - x = 2$

Subtract $x$ from $8 x$ .

$7 x - 2 = 2$

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

Add $2$ to both sides of the equation.

$7 x = 2 + 2$

Add $2$ and $2$ .

$7 x = 4$

Divide each term in $7 x = 4$ by $7$ and simplify.

Divide each term in $7 x = 4$ by $7$ .

$\frac{7 x}{7} = \frac{4}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{4}{7}$

Divide $x$ by $1$ .

$x = \frac{4}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{7}$

Decimal Form:

$x = 0.\overline{571428}$

Solve for x 36^(4x-1)=6^(x+2)

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