107k views
2 votes
Evaluate exactly the expression given that logM=2.9 and logN=−3.5. log(0.1M^6N^5)=

User MendyK
by
8.0k points

1 Answer

4 votes

Answer:

Given:

logM = 2.9

logN = -3.5

We want to find the value of log(0.1M^6N^5).

Using logarithmic properties, we can rewrite the expression as:

log(0.1M^6N^5) = log(0.1) + log(M^6) + log(N^5)

Now, let's substitute the given values:

log(0.1M^6N^5) = log(0.1) + log(M^6) + log(N^5)

= log(0.1) + 6log(M) + 5log(N)

Substituting the values logM = 2.9 and logN = -3.5:

log(0.1M^6N^5) = log(0.1) + 6(2.9) + 5(-3.5)

= log(0.1) + 17.4 - 17.5

= log(0.1) - 0.1

Now, using logarithmic properties, we know that log(0.1) = -1:

log(0.1M^6N^5) = -1 - 0.1

= -1.1

Therefore, the value of log(0.1M^6N^5) is -1.1.

Explanation:

To evaluate the expression log(0.1M^6N^5), we can use logarithmic properties to simplify it. Let's substitute the given values logM = 2.9 and logN = -3.5 into the expression:

log(0.1M^6N^5) = log(0.1) + log(M^6) + log(N^5)

Using the properties of logarithms, we can rewrite this expression as:

log(0.1M^6N^5) = log(0.1) + 6log(M) + 5log(N)

Substituting the given values, we have:

log(0.1M^6N^5) = log(0.1) + 6(2.9) + 5(-3.5)

Now, we can evaluate this expression:

log(0.1M^6N^5) = log(0.1) + 17.4 - 17.5

Using logarithmic properties, log(0.1) is equal to -1:

log(0.1M^6N^5) = -1 + 17.4 - 17.5

Simplifying further:

log(0.1M^6N^5) = -0.1

Therefore, log(0.1M^6N^5) is equal to -0.1.

User Tanuki
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories