How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?

• carlosego: Some of the logarithmic properties most used to solve equations are the following.
   1) log (a) ^ b = b * log (a)
   2) log (a * b) = log (a) + log (b)
   3) log (a / b) = log (a) - log (b)
   These logarithmic properties can be used to solve equations.
   For example:
   2 ^ x = 56
   If we apply to this equation the logarithm function on both sides that we have left
   log (2) ^ x = log (56)
   This function is equivalent to the first.
   If we now apply the property 1) of the previous logarithms, we can reveal x of the equation.
   x * log (2) = log (56)
   x = log (56) / log (2)
   x = 5,807
   Thus, thanks to the properties of the logarithms, this exponential function could be solved