10) 7^(x+1) = (1/7)^x

1. Rewrite the right side with base 7: $$7^{x+1} = (7^{-1})^x$$

2. Simplify: $$7^{x+1} = 7^{-x}$$

3. Equate exponents: $$x+1 = -x$$

4. Solve for x: $$2x = -1 > x = -1/2$$.