Final answer:
Logarithmic functions are inverse functions to exponential functions and are used to solve equations and represent exponential growth and decay. To solve logarithmic equations, you can use logarithmic properties or convert them to exponential form. The measure of an interior angle of a polygon with 20 diagonals is 135°.
Step-by-step explanation:
In mathematics, a logarithmic function is an inverse function to an exponential function. Logarithmic functions are used to solve equations and represent exponential growth and decay. The most commonly used logarithmic function is the common logarithm which is denoted as log10 or simply log. To solve logarithmic equations, you can either use logarithmic properties or convert them to exponential form.
Now, let's calculate the measure of an interior angle of a polygon with 20 diagonals:
- First, we know that the number of diagonals in a polygon with n sides can be calculated using the formula D = n(n-3)/2.
- Substituting the given number of diagonals (20) into the formula D = n(n-3)/2, we get: 20 = n(n-3)/2.
- Multiplying both sides of the equation by 2 to eliminate the fraction, we obtain: 40 = n(n-3).
- Simplifying further, we have the quadratic equation n^2 - 3n - 40 = 0.
- Next, we can solve this quadratic equation by factoring or using the quadratic formula.
- Factoring the equation, we get (n - 8)(n + 5) = 0.
- This gives us two possible solutions: n - 8 = 0 (n = 8) or n + 5 = 0 (n = -5). Since we are dealing with the number of sides of a polygon, we take the positive solution n = 8.
- Finally, we can calculate the measure of an interior angle using the formula: A = (n-2) * 180° / n.
- Substituting the value of n (8) into the formula, we get A = (8-2) * 180° / 8 = 6 * 180° / 8 = 135°.