Use the rules of logarithms to write the following expression in terms of ln(𝑥) and ln(𝑦).ln(𝑥3𝑦)=
Question
Use the rules of logarithms to write the following expression in terms of ln(𝑥) and ln(𝑦).
Solution
The expression can be simplified using the properties of logarithms.
The properties we will use are:
- ln(a*b) = ln(a) + ln(b)
- ln(a^n) = n*ln(a)
Applying these properties to the expression ln(x^3*y), we get:
ln(x^3*y) = ln(x^3) + ln(y)
Then, applying the second property to ln(x^3), we get:
ln(x^3y) = 3ln(x) + ln(y)
So, ln(x^3y) can be written in terms of ln(x) and ln(y) as 3ln(x) + ln(y).
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