e^(q/y) = x1 + 1 in terms of y
You bots clearly cannot interpret parentheses.
e^(q/y) = x1 + 1
e^(q/y) = x1 + 1
q/y = ln(x1 + 1)
y = q/ln(x1 + 1)
oops - my bad. And you didn't catch it!
e^(q/y) = x1 + 1
e^(q/y) = x1 - 1
q/y = ln(x1 - 1)
y = q/ln(x1 - 1)
Apologies for the oversight. You are correct. Given the equation e^(q/y) = x1 - 1, we can solve for y as follows:
1. Take the natural logarithm (ln) of both sides of the equation:
ln(e^(q/y)) = ln(x1 - 1)
2. Use the logarithmic property ln(e^a) = a:
q/y = ln(x1 - 1)
3. Multiply both sides of the equation by y to isolate y:
y*(q/y) = y*ln(x1 - 1)
4. Simplify the left side of the equation:
q = y*ln(x1 - 1)
5. Divide both sides of the equation by ln(x1 - 1) to solve for y:
y = q/ln(x1 - 1)
Therefore, y is equal to q divided by the natural logarithm of (x1 - 1).
To isolate y on one side of the equation, we can start by subtracting 1 from both sides:
e^(q/y) - 1 = x1
Next, we can multiply both sides by y to move the y in the denominator:
y*(e^(q/y) - 1) = x1
Expanding the expression on the left side:
y*e^(q/y) - y = x1
Now, to isolate y, we can move the term - y to the other side by adding y to both sides:
y*e^(q/y) = x1 + y
Finally, we can divide both sides by e^(q/y):
y = (x1 + y) / e^(q/y)
To express the equation e^(q/y) = x1 + 1 in terms of y, we need to isolate the variable y on one side of the equation. Here's how you can do it:
1. Start by subtracting 1 from both sides of the equation:
e^(q/y) - 1 = x1
2. Next, we need to get rid of the exponential term on the left-hand side. To do that, we can take the natural logarithm (ln) of both sides of the equation:
ln(e^(q/y) - 1) = ln(x1)
3. Applying the logarithm property, ln(e^a) = a, where a is any real number, we simplify the left-hand side:
q/y - 1 = ln(x1)
4. Now, let's isolate y by moving the -1 to the other side of the equation:
q/y = ln(x1) + 1
5. Finally, multiply both sides of the equation by y:
q = y * (ln(x1) + 1)
Therefore, the equation e^(q/y) = x1 + 1 can be expressed in terms of y as q = y * (ln(x1) + 1).
To solve for y in terms of x1, we have the equation e^(q/y) = x1 + 1.
Step 1: Start by subtracting 1 from both sides of the equation to isolate the exponential term:
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: Simplify the left side of the equation using the logarithmic property ln(e^a) = a:
q/y - 1 = ln(x1)
Step 4: Add 1 to both sides of the equation to isolate the fraction:
q/y = ln(x1) + 1
Step 5: Multiply both sides of the equation by y to eliminate the fraction:
q = y(ln(x1) + 1)
Step 6: Finally, divide both sides of the equation by ln(x1) + 1 to solve for y:
y = q/(ln(x1) + 1)
Therefore, y is equal to q divided by the natural logarithm of (x1 + 1).
Apologies for the confusion in my previous response. You are correct. Given the equation e^(q/y) = x1 + 1, we can solve for y as follows:
1. Take the natural logarithm (ln) of both sides of the equation:
ln(e^(q/y)) = ln(x1 + 1)
2. Use the logarithmic property ln(e^a) = a:
q/y = ln(x1 + 1)
3. Multiply both sides of the equation by y to isolate y:
y*(q/y) = y*ln(x1 + 1)
4. Simplify the left side of the equation:
q = y*ln(x1 + 1)
5. Divide both sides of the equation by ln(x1 + 1) to solve for y:
y = q/ln(x1 + 1)
Therefore, y is equal to q divided by the natural logarithm of (x1 + 1).