Solve for x 2^(3x-21)+2=66

$2^{3 x - 21} + 2 = 66$

Step 1

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

Subtract $2$ from both sides of the equation.

$2^{3 x - 21} = 66 - 2$

Subtract $2$ from $66$ .

$2^{3 x - 21} = 64$

Step 2

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

$2^{3 x - 21} = 2^{6}$

Step 3

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

$3 x - 21 = 6$

Step 4

Solve for $x$ .

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

Add $21$ to both sides of the equation.

$3 x = 6 + 21$

Add $6$ and $21$ .

$3 x = 27$

Divide each term in $3 x = 27$ by $3$ and simplify.

Divide each term in $3 x = 27$ by $3$ .

$\frac{3 x}{3} = \frac{27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{27}{3}$

Divide $x$ by $1$ .

$x = \frac{27}{3}$

Simplify the right side.

Divide $27$ by $3$ .

$x = 9$