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Find the value of n that satisfies the equation 2(-3)4n = 18(27)n+2
- a)3
- b)4
- c)6
- d)8
- e)22
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the value of n that satisfies the equation 2(-3)4n = 18(27)n+2a)3...
We need to find the value of n, given 2(−34n)=18(27)n+2
(Cancelling 2 on both sides. Also making use of the fact that 32k = (-3)2k)
Most Upvoted Answer
Find the value of n that satisfies the equation 2(-3)4n = 18(27)n+2a)3...
**Problem**
Find the value of n that satisfies the equation 2(-3)4n = 18(27)n 2.
**Solution**
Let's simplify the given equation first.
2(-3)4n = 18(27)n 2
2(-81)n = 18(729)n
-162n = 162n
n = -1/2
Now, we need to check if this value of n satisfies the original equation.
2(-3)4(-1/2) = 18(27)(-1/2) 2
2(-3)-2 = 18(27)(1/4)
2(1/9) = 18(1/4)
2/9 = 9/2
Since the left-hand side and right-hand side of the equation are not equal, the value of n = -1/2 does not satisfy the equation.
Therefore, there is no solution for the given equation.
**Answer**
Option (e) None of the above.
Find the value of n that satisfies the equation 2(-3)4n = 18(27)n 2.
**Solution**
Let's simplify the given equation first.
2(-3)4n = 18(27)n 2
2(-81)n = 18(729)n
-162n = 162n
n = -1/2
Now, we need to check if this value of n satisfies the original equation.
2(-3)4(-1/2) = 18(27)(-1/2) 2
2(-3)-2 = 18(27)(1/4)
2(1/9) = 18(1/4)
2/9 = 9/2
Since the left-hand side and right-hand side of the equation are not equal, the value of n = -1/2 does not satisfy the equation.
Therefore, there is no solution for the given equation.
**Answer**
Option (e) None of the above.
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