Question

Write as a single term (3(2ln(x-1) - ln(x)) + ln(x-1)).

A. ( 3ln(x-1) )
B. ( 2ln(x-1) )
C. ( ln(x-1) )
D. ( 4ln(x-1) )

Answer 1

To write the expression as a single term, we can combine the ln terms using logarithmic properties. The expression can be written as 7ln(x-1) - 3ln(x).

Step-by-step explanation:

To write the expression as a single term, we can simplify the given expression by combining the ln terms using the properties of logarithms. The expression is:

3(2ln(x-1) - ln(x)) + ln(x-1)

= 3 * 2ln(x-1) - 3ln(x) + ln(x-1)

= 6ln(x-1) - 3ln(x) + ln(x-1)

= (6ln(x-1) + ln(x-1)) - 3ln(x)

= 7ln(x-1) - 3ln(x)

Therefore, the expression can be written as a single term as 7ln(x-1) - 3ln(x).