Question

Condense the expression to a single logarithm using the properties of logarithms.

log(x)−1/2log(y)+5log(z)

Answer 1

To condense the given expression, we can break it down into separate logarithms using the properties of logarithms and then combine them into a single logarithm.

Step-by-step explanation:

To condense the expression log(x)−1/2log(y)+5log(z) to a single logarithm, we can use the properties of logarithms. Let's break it down step by step:

1. The property log(xy) = log(x) + log(y) allows us to split the expression into three separate logarithms: log(x), -1/2log(y), and 5log(z).
2. Next, we can rewrite -1/2log(y) as log(y^(-1/2)).
3. Using the property log(a^b) = b*log(a), we can further simplify log(y^(-1/2)) to -1/2log(y).
4. Finally, we can combine all the logarithms into a single logarithm by using the property log(a) + log(b) = log(ab). So, the condensed expression becomes log(x) + log(y^(-1/2)) + log(z^5), which can be further simplified to log(x) + log(y^(-1/2)z^5).