Write the equivalent logarithmic statement for 53 = 125 and the equivalent exponential statement for 5 (1)/(5) = -1.

If $b^y = x$, then $\log_b x = y$. $\log_5 125 = 3$ The equivalent logarithmic statement is $\boxed{\log_5 125 = 3}$.

**b)** $y^x = z$

If $b^y = x$, then $\log_b x = y$. $\log_y z = x$ The equivalent logarithmic statement is $\boxed{\log_y z = x}$.

2. Write the equivalent exponential statement for each of the following:

   a) $\log_5 \frac{1}{5} = -1$

If $\log_b x = y$, then $b^y = x$. $5^{-1} = \frac{1}{5}$ The equivalent exponential statement is $\boxed{5^{-1} = \frac{1}{5}}$.

**b)** $\log_9 3 = \frac{1}{2}$

If $\log_b x = y$, then $b^y = x$. $9^{1/2} = 3$ The equivalent exponential statement is $\boxed{9^{1/2} = 3}$.

**c)** $\log_5 625 = 4$

If $\log_b x = y$, then $b^y = x$. $5^4 = 625$ The equivalent exponential statement is $\boxed{5^4 = 625}$.

3. Solve for $x$ in the following exponential equations:

   a) $2^{x-1} = 64$