Answer :
Answer:
Step-by-step explanation:To solve for \( y \) in the equation \( (x-1)^y = (x+1)^x \), given that \( x \neq 0, -1 \), let's proceed step by step.
Given equation:
\[ (x-1)^y = (x+1)^x \]
To find \( y \), we can take the natural logarithm (ln) of both sides:
\[ \ln((x-1)^y) = \ln((x+1)^x) \]
Apply the power rule of logarithms:
\[ y \ln(x-1) = x \ln(x+1) \]
Now, solve for \( y \):
\[ y = \frac{x \ln(x+1)}{\ln(x-1)} \]
Therefore, \( y = \frac{x \ln(x+1)}{\ln(x-1)} \) is the solution for \( y \) in terms of \( x \), under the condition \( x \neq 0, -1 \).
Answer:
Given the equation:
x-1/y = X/x+1
We want to solve for ( y ) given that ( x ) is not 0 or -1. First, we'll cross-multiply to eliminate the fractions:
(x-1)(x+1) = y. X
Simplify the left-hand side:
x² - 1 = y . X
Now, solve for ( y ):
y = x² - 1/X
Thus, the value of ( y ) is:
y = x² - 1/X