2. Express the following logarithms in terms of ln 5 and ln 7....

Question

2. Express the following logarithms in terms of ln 5 and ln 7.

f. (ln35 + ln(1/7))/(ln25)

Accepted Answer

Welcome back to another video. Express the following expression in terms of LN of 2 and LN of 5. LN of 50 plus Llan of 2 divided by 5 divided by LN of 25. It says 1/2 plus LN of 2 divided by LN of 5, B 1/2 + 2 LN of 2 divided by LN of 5, C 1 plus Llan of 2 divided by LN of 5, and DLN of 2 divided by LN of 5. So for this problem, let's analyze each number and let's express these numbers. In terms of their prime factors, because 2 and 5 are prime numbers, right? So it would be helpful to analyze each, starting with 50. It can be written as 2 multiplied by 25, which is 2 multiplied by 5 squared. Then we have 25, which is just 5 square. And now what we can do is consider each logarithm, starting with LN of 50, that's LN 2 multiplied by 5 squad. We can apply the product rule of logarithms to rewrite it as a sum, that's a line of 2 plus. A length of 5 squared. And for Alana 5 squad, we can also apply the power rule. So that the final form of Llan of 50 would be Llan of 2 + 2 of 5. Similarly, Alan of 25 is LN of 52. We can again apply the power rule to get to Alana of 5. What about a land of 2 divided by 5? While here, we can apply the quotient rule because we have a ratio. So we take a line of 2 and subtract a line of 5. And then we can substitute everything into the original form. Starting with LN of 50, we're going to write LN of 2 + 2 LN of 5. We are adding LN of 2 divided by 5, which is LN of 2 minus LN of 5, and we're dividing by LN of 25, which is 2 LN of 5. In the numerator, let's combine the like terms. We're going to get to a line of 2. Plus alan of 5 divided by 2 of 5. And now let's divide. LA 5 divided by LA of 5 is 1, so we get 1/2. Plus 2 LN of 2 divided by 2 LN of 5 is going to be LN of 2 divided by LN of 5. Now, let's consider the answer choices. We can conclude that the correct answer to this problem corresponds to the answer choice A. Thank you for watching.

2. Express the following logarithms in terms of ln 5 and ln 7.f. (ln35 + ln(1/7))/(ln25)

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2. Express the following logarithms in terms of ln 5 and ln 7.
f. (ln35 + ln(1/7))/(ln25)