Final answer:
To evaluate logarithms, we apply rules such as the sum of logs for products, the difference of logs for quotients, and the multiplier for exponents within logs, using the given that log a(x) = 5.2.
Step-by-step explanation:
To evaluate logarithms using properties of logarithms and given facts, we apply several important rules. The first rule is that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log xy = log x + log y. Similarly, the logarithm of a quotient is the difference of the logarithms: log(x/y) = log x - log y. When a number is raised to an exponent within a logarithm, the exponent can come out in front as a multiplier: log(x^n) = n * log x.
Using the given fact that loga(x) = 5.2, we can solve various expressions involving logarithms. For example, the logarithm of a product involving x would use the summing property, while the logarithm of a quotient would use the difference property. If x is raised to an exponent in the logarithm, we would multiply that exponent by 5.2 to find the value. These properties allow us to evaluate more complex logarithmic expressions.