Write the following expression in terms of ln(𝑥), ln(𝑥+1), and/or ln(𝑥+2). Expand and simplify your answer.ln(𝑥(𝑥+1)(𝑥+2))
Question
Write the following expression in terms of ln(𝑥), ln(𝑥+1), and/or ln(𝑥+2). Expand and simplify your answer.ln(𝑥(𝑥+1)(𝑥+2))
Solution
The expression ln(x(x+1)(x+2)) can be simplified using the properties of logarithms.
Step 1: Apply the property of logarithms that states ln(abc) = ln(a) + ln(b) + ln(c).
ln(x(x+1)(x+2)) = ln(x) + ln(x+1) + ln(x+2)
So, the simplified expression of ln(x(x+1)(x+2)) in terms of ln(x), ln(x+1), and ln(x+2) is ln(x) + ln(x+1) + ln(x+2).
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