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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
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