in the equation e^(q/y) = x1 + 1, isolate the y variable
To isolate the variable y in the equation e^(q/y) = x1 + 1, we can follow these steps:
1. Start by subtracting 1 from both sides of the equation:
e^(q/y) - 1 = x1
2. In order to get rid of the exponent, take the natural logarithm (ln) of both sides:
ln(e^(q/y) - 1) = ln(x1)
3. By using the property of logarithms, ln(e^a) equals a, and ln(a - b) cannot be simplified further:
(q/y) - 1 = ln(x1)
4. Now, add 1 to both sides of the equation:
(q/y) = ln(x1) + 1
5. Finally, isolate y by multiplying both sides of the equation by y:
q = y * (ln(x1) + 1)
Thus, the y variable is isolated as:
y = q / (ln(x1) + 1)
To isolate the y variable in the equation e^(q/y) = x1 + 1, we need to perform several steps.
Step 1: Start by subtracting 1 from both sides of the equation to isolate e^(q/y) on the left-hand side:
e^(q/y) - 1 = x1
Step 2: Next, take the natural logarithm (ln) of both sides of the equation to remove the exponential term:
ln(e^(q/y) - 1) = ln(x1)
Step 3: Use the logarithmic property ln(e^a) = a to simplify the left-hand side:
q/y - ln(1) = ln(x1)
q/y - 0 = ln(x1)
Step 4: Simplify further by removing the zero term:
q/y = ln(x1)
Step 5: Finally, multiply both sides of the equation by y to isolate the y variable:
q = y * ln(x1)
So, the isolated y variable in the equation e^(q/y) = x1 + 1 is y = q / ln(x1).
To isolate the y variable in the equation e^(q/y) = x1 + 1, you can follow these steps:
Step 1: Start by subtracting 1 from both sides to get rid of the constant term on the right side of the equation:
e^(q/y) - 1 = x1
Step 2: Take the natural logarithm (ln) of both sides of the equation to eliminate the exponential term:
ln(e^(q/y) - 1) = ln(x1)
Step 3: Use the logarithmic property that ln(e^z) = z:
q/y - 1 = ln(x1)
Step 4: Next, isolate the q/y term by adding 1 to both sides of the equation:
q/y = ln(x1) + 1
Step 5: Finally, multiply both sides of the equation by y to solve for y:
y(q/y) = yln(x1) + y
q = yln(x1) + y
Therefore, the equation that isolates the y variable is q = yln(x1) + y.