Eric S.

asked • 01/26/24

precalculus questions

having a hard time getting a few questions answered and understanding how to get the correct answers.


  1. first problem:


Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

 

ln(1/25^k)

 

Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*ln(h).


2. second question:


Use the properties of logarithms to expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

 

log(√x^3y^-4)







 





2 Answers By Expert Tutors

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Oziel T. answered • 01/27/24

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Here is the explanation to these two problems. Sorry for the lengthy video. I wanted to clearly explain how to do this. I hope this helps!

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Brenda D.

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I agree with your process and illustration of the rules but shouldn’t you expand the base further in question 1. I asked because the question does say to expand the logarithm as much as possible.
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01/27/24

Mark M. answered • 01/26/24

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Retired math prof. Very extensive Precalculus tutoring experience.

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ln(1 / (25)k) = ln(1) - ln(25)k = 0 - k ln(25) = -kln(25)


log(√(x3) y-4) = log(√x3) + log(y-4) = log(x3/2) + log(y-4) = (3/2)logx - 4logy

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Bradford T.

You could continue with the first one using 25=5^2 to get -2kln(5)
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01/26/24

Eric S.

Thank you for your response. I tried plugging those answers in to complete the questions with those answers and it is not taking them as the correct answer. I will try again later but I don't know if maybe I am just inputting the information incorrectly.
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01/27/24

Oziel T.

tutor
I thought the second one had (x^3y^-4) all inside the square root... am I wrong?
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01/27/24

Mark M.

tutor
Is the first one ln(1/(25)^k) or ln((1/25)^k)? Also, if Oziel T. is correct, then the answer would not be the same as mine. Parentheses are important.
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01/27/24

Brenda D.

tutor
I agree with Oziel T. My questions are for Eric S. Can you clarify the expressions further by answering, Oziel T., above? I know it can be difficult to enter the problems exactly as they are presented to you and sometimes one is forced to do what their keyboard’s allow. When you said you tried plugging those answers in were you referring to Mark M’s answers only. I don’t know how many tries you get for your input. Were you able to try Bradford T’s further expansion of the base as input? Also can you give an example of the format acceptable as answers for your input? Often just a little more input from the student helps a lot.
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01/27/24

Eric S.

I will check again on both I am pretty sure I copied the both problems to each question the way that I was given but I will recheck since the response answers came up not correct. I could be missing something myself.
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01/28/24

Eric S.

I just checked and the First problem does put the problem to solve as ln(1/25^k) and yes I tried putting in the answer of -k*ln(25) and also tried -2k*ln(5). Neither answer was correct. No limit on how many attempts I can try and the question for the first problem is exactly written down exactly as it is given.
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01/28/24

Eric S.

for the second question the equation that I need to resolve is indeed log(square root of x^3y^-4) which is also is not taking the answer given as correct.
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01/28/24

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