Answer :
Answer:
To find the value of \( n \) from the equation \( 22^{n-1} = 83 - n \), we will solve step by step:
Given equation:
\[ 22^{n-1} = 83 - n \]
Let's test integer values of \( n \) to find a solution.
For \( n = 3 \):
\[ 22^{3-1} = 22^2 = 484 \]
\[ 83 - 3 = 80 \]
Clearly, \( 22^2 = 484 \) and \( 83 - 3 = 80 \), which are not equal.
For \( n = 2 \):
\[ 22^{2-1} = 22^1 = 22 \]
\[ 83 - 2 = 81 \]
Again, \( 22^1 = 22 \) and \( 83 - 2 = 81 \), which are not equal.
For \( n = 1 \):
\[ 22^{1-1} = 22^0 = 1 \]
\[ 83 - 1 = 82 \]
Here, \( 22^0 = 1 \) and \( 83 - 1 = 82 \), which are not equal.
Let's try \( n = 0 \):
\[ 22^{0-1} = 22^{-1} = \frac{1}{22} \]
\[ 83 - 0 = 83 \]
Here, \( 22^{-1} = \frac{1}{22} \) and \( 83 - 0 = 83 \), which are not equal.
For \( n = 1 \):
\[ 22^{1-1} = 22^0 = 1 \]
\[ 83 - 1 = 82 \]
Here, \( 22^0 = 1 \) and \( 83 - 1 = 82 \), which are not equal
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Answer:
84/23
Step-by-step explanation:
22n-1=83-n
or , 22n+n = 83+1
or , 23n=84
or, n=84/23