Final answer:
The question involves understanding the properties of exponential and logarithmic functions, f(x) = 10⁻⁽ and g(x) = log(x), which are inverse functions. This means applying a logarithm to an exponential function returns the original exponent, demonstrating the close relationship between these two mathematical concepts.
Step-by-step explanation:
Understanding Exponential and Logarithmic Functions
The question involves two types of functions - exponential and logarithmic. Specifically, we are dealing with f(x) = 10⁻⁽ and g(x) = log(x). The exponential function f(x) represents growth or decay processes where the rate of change is proportional to the value of the function. On the other hand, the logarithmic function g(x) is the inverse of the exponential function and is used to solve for the exponent in equations like 10⁻⁽ = x.
To solve the mathematical problem completely, let's analyze the properties and relationships between these functions. According to the information given, if a and b are true, then c is true as well, based on logical conclusions. If we consider 'gazintz' as f(x) and 'gazatz' as g(x), and since all gazintz are gazatz and all gazatz are garingers, we can conclude all gazintz are garingers. This relates to the fact that exponential and logarithmic functions are inverses of each other, which means applying a logarithm to an exponential function will yield the original exponent.
For instance, if you have y = 10⁻⁽, then taking the logarithm of both sides gives you log(y) = x, demonstrating the inverse relationship. Also, the property referenced from Figure 3.3 and 3.4, log(ab) = log(a) + log(b), is applicable here, further illustrating how logarithms can break down multiplication into addition. Additionally, the relationship between logarithms and exponents is highlighted in statement 3, showing that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log(a⁻⁽) = n × log(a)).