SOLUTION: Hello, hope everyone is doing alright. This is my first time here so I apologize for poor formatting. This is the question I have. "Write the logarithmic expression as a single

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, hope everyone is doing alright. This is my first time here so I apologize for poor formatting. This is the question I have. "Write the logarithmic expression as a single       Log On


   

Question 1080107: Hello, hope everyone is doing alright. This is my first time here so I apologize for poor formatting. This is the question I have.
"Write the logarithmic expression as a single logarithm with a coefficient of 1"
2/3In(x-1)+4In(x+5)-1/2In(x-4)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see the following worksheet.

in general:

b*ln(a) is equal to ln(a^b)

d*ln(c) is equal to ln(c^d)

f*ln(e) is equal to ln(e^f)

ln(a^b) + ln(c^d) is equal to ln(a^b * c^d)

ln(a^b * c^d) - ln(e^f) is equal to ln(a^b * c^d / e^f)

that's what's done in the worksheet shown below:

$$$

you can confirm the solution is correct by choosing any valid value of x and evaluating the original function and the final function.

the answer should be the same.

i did so with x = 12 and got 11.89172945 when evaluating both functions.

consequently i'm reasonably sure the translation from the original function to the final function was successful.