Final answer:
The condensed expression for 3logx - log2 is log(x^3 / 2) by applying the power rule and the division rule of logarithms.
Step-by-step explanation:
The question asks for the condensed expression for 3logx - log2. According to the properties of logarithms, specifically the power rule, which says the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can apply this to condense the expression. Furthermore, the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers allows us to combine the two terms into one logarithmic expression.
Using these properties, the condensed expression becomes log(x3 / 2). Here's the breakdown:
- We can rewrite 3logx as log(x3) because of the power rule of logarithms.
- Next, we understand that subtracting logarithms with the same base equates to the division of the arguments, in this case, log(x3) - log(2) becomes log(x3 / 2).