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

Accepted Solution

 It is called the exponential function of base a, to that whose generic form is f (x) = a ^ x, being a positive number other than 1.
 Every exponential function of the form f (x) = a^x, complies with the followingProperties:
 1. The function applied to the zero value is always equal to 1: f (0) = a ^ 0  = 1
 2. The exponential function of 1 is always equal to the base: f (1) = a ^ 1  = a.
 3. The exponential function of a sum of values is equal to the product of the application of said function on each value separately.
 f (m + n) = a ^ (m + n) = a ^ m · a ^ n
 = f (m) · f (n).
 4. The exponential function of a subtraction is equal to the quotient of its application to the minuend divided by the application to the subtrahend:
 f (p - q) = a ^ (p - q) = a ^ p / a ^ q
 In the loga (b), a is called the base of the logarithm and b is called an argument, with a and b positive.
 Therefore, the definition of logarithm is:
 loga b = n ---> a ^ n = b (a> 0, b> 0)