Question

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

Answer 1

Exponential:
 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
 Logarithm:
 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)