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.

$\ln(x(x+1)(x+2))$

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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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