MATH SOLVE

4 months ago

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

Accepted Solution

A:

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)

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)