Expand the logarithm fully using the properties of logs. Express the final answer in terms of log, xlogx, and log, ylogy.log, x, squared, ylogx 2 y
Question
Expand the logarithm fully using the properties of logs.
Express the final answer in terms of log, xlogx, and log, ylogy.log, x, squared, ylogx 2 y.
Solution
The given expression is log(x^2y).
We can use the properties of logarithms to expand this expression.
The properties we will use are:
- log(a*b) = log(a) + log(b)
- log(a^n) = n*log(a)
Applying these properties, we get:
log(x^2y) = log(x^2) + log(y)
Now, we can apply the second property to log(x^2):
log(x^2) = 2*log(x)
So, the fully expanded expression is:
2*log(x) + log(y)
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