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.