Solve 3^x-a=6(3^x-b)

$$3 ^ { x } - a = 6 ( 3 ^ { x } - b )$$

Solve for a

$$a=6b-5\times 3^{x}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by 3^{x}-b.

$$3^{x}-a=6\times 3^{x}-6b$$

Subtract 3^{x} from both sides.

$$-a=6\times 3^{x}-6b-3^{x}$$

Combine 6\times 3^{x} and -3^{x} to get 5\times 3^{x}.

$$-a=5\times 3^{x}-6b$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{5\times 3^{x}-6b}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{5\times 3^{x}-6b}{-1}$$

Divide 5\times 3^{x}-6b by -1.

$$a=6b-5\times 3^{x}$$

Solve for b

$$b=\frac{5\times 3^{x}+a}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by 3^{x}-b.

$$3^{x}-a=6\times 3^{x}-6b$$

Swap sides so that all variable terms are on the left hand side.

$$6\times 3^{x}-6b=3^{x}-a$$

Subtract 6\times 3^{x} from both sides.

$$-6b=3^{x}-a-6\times 3^{x}$$

Combine 3^{x} and -6\times 3^{x} to get -5\times 3^{x}.

$$-6b=-5\times 3^{x}-a$$

Divide both sides by -6.

$$\frac{-6b}{-6}=\frac{-5\times 3^{x}-a}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$b=\frac{-5\times 3^{x}-a}{-6}$$

Divide -5\times 3^{x}-a by -6.

$$b=\frac{5\times 3^{x}+a}{6}$$