Solve for x 3^(x-7)=27^(2x)

$3^{x - 7} = 27^{2 x}$

Step 1

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

$3^{x - 7} = 3^{3 (2 x)}$

Step 2

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

$x - 7 = 3 (2 x)$

Step 3

Solve for $x$ .

Multiply $2$ by $3$ .

$x - 7 = 6 x$

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

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

$x - 7 - 6 x = 0$

Subtract $6 x$ from $x$ .

$- 5 x - 7 = 0$

Add $7$ to both sides of the equation.

$- 5 x = 7$

Divide each term in $- 5 x = 7$ by $- 5$ and simplify.

Divide each term in $- 5 x = 7$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{7}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{7}{- 5}$

Divide $x$ by $1$ .

$x = \frac{7}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{5}$

Decimal Form:

$x = - 1.4$

Mixed Number Form:

$x = - 1 \frac{2}{5}$