Final answer:
To write 4logx - (1/2)logy + 5logx as the logarithm of a single expression, we can use the properties of logarithms. First, combine the terms using the sum of logarithms property. Then, simplify using the product of logarithms property. Finally, subtract the term using the difference of logarithms property.
Step-by-step explanation:
To write 4logx - (1/2)logy + 5logx as the logarithm of a single expression, we can use the logarithmic properties.
- Start by applying the property that the logarithm of a product is the sum of the logarithms of the individual factors. So, 4logx + 5logx can be written as logx^4 + logx^5.
- Next, use the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. So, logx^4 + logx^5 becomes 4logx + 5logx.
- Finally, apply the property that the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So, subtract (1/2)logy from 4logx + 5logx to get 4logx + 5logx - (1/2)logy.