Solve the following exponential equations: a) 8^x = (1)/(4) b) 5^x+1 = 125 c) 32x−1 = (1)/(27) d) 2^x+2 = 6 e) 3^x−3 = 6

$$3x = -2$$ $$x = -\frac{2}{3}$$

The solution is $\boxed{x = -\frac{2}{3}}$.

$$x+1 = 3$$ $$x = 3-1$$ $$x = 2$$

The solution is $\boxed{x = 2}$.

$$2x-1 = -3$$ $$2x = -3+1$$ $$2x = -2$$ $$x = -1$$

The solution is $\boxed{x = -1}$.

Using $\log_2$ is convenient here.

$$\log_2(2^{x+2}) = \log_2(6)$$

$$x = \log_2(6) - 2$$

The solution is $\boxed{x = \log_2(6) - 2}$.

Using $\log_3$ is convenient here.

$$\log_3(3^{x-3}) = \log_3(6)$$

$$x = \log_3(6) + 3$$

The solution is $\boxed{x = \log_3(6) + 3}$.