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).ln(𝑥3𝑦)=
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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