1) how can the properties of exponents solve logarithmic equations?
2) how can the properties of exponents solve exponential equations?

The properties of exponents help solve logarithmic and exponential equations by:
a. Multiplication inside the log can be turned into addition outside the log, and vice versa.
b. Division inside the log can be turned into subtraction outside the log, and vice versa.
c. An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.