Given ln(m)=4,ln(n)=−7 and ln(p)=−8, evaluate:
ln(e^7n^4/sqrt(mp))
can you explain how to get the answer ..thanks
jonathan
2 hours ago
Use your log rules ...
ln(e^7n^4/sqrt(mp))
= ln (e^7) + ln (n^4) - ln (mp)^(1/2)
= 7lne + 4ln n - (1/2) (ln m + ln p)
now just sub in the given values, remember that ln e = 1
mathhelper
1 hour ago
is it -19?
clearly, yes.
To evaluate the expression ln(e^7n^4/sqrt(mp)), we will substitute the given values into the expression we derived earlier.
First, let's substitute the values of ln(m), ln(n), and ln(p):
ln(e^7n^4/sqrt(mp)) = 7ln(e) + 4ln(n) - (1/2)(ln(m) + ln(p))
Since ln(e) = 1, this simplifies to:
ln(e^7n^4/sqrt(mp)) = 7 + 4ln(n) - (1/2)(ln(m) + ln(p))
Now we substitute the given values ln(n) = -7, ln(m) = 4, and ln(p) = -8:
ln(e^7n^4/sqrt(mp)) = 7 + 4(-7) - (1/2)(4 + (-8))
= 7 - 28 - (1/2)(-4)
= 7 - 28 + 2
= -19 + 2
= -17
Thus, ln(e^7n^4/sqrt(mp)) evaluates to -17.
To evaluate the expression ln(e^7n^4/sqrt(mp)), we can follow these steps:
1. Apply the rule ln(a/b) = ln(a) - ln(b) to split the expression into three separate terms:
ln(e^7) + ln(n^4) - ln(sqrt(mp))
2. Apply the rule ln(a^n) = nln(a) to simplify each term:
7ln(e) + 4ln(n) - (1/2)(ln(m) + ln(p))
3. Since ln(e) is the natural logarithm of the Euler's number, e, it is equal to 1:
7(1) + 4ln(n) - (1/2)(ln(m) + ln(p))
4. Substitute the given values: ln(m) = 4, ln(n) = -7, ln(p) = -8:
7 + 4(-7) - (1/2)(4 + -8)
5. Simplify:
7 - 28 - (1/2)(-4)
-21 - (-2)
-21 +2
-19
Therefore, the value of ln(e^7n^4/sqrt(mp)) is -19.