Question

Make x the subject of, without solving, y = b*ln(x) + 3.

a) x = e^(y - 3)/b
b) x = (y - 3)/(bln)
c) x = e^(y - 3b)
d) x = (y - 3 - ln)/b

Answer 1

To make x the subject of the equation y = b*ln(x) + 3, you subtract 3 from both sides, divide by b, and then use the property that e and ln are inverse functions, resulting in x = e^((y - 3) / b).

Step-by-step explanation:

To make x the subject of the equation y = b*ln(x) + 3, we need to isolate x on one side of the equation. Here is a step-by-step process:

1. Start with the equation: y = b*ln(x) + 3.
2. Subtract 3 from both sides to get: y - 3 = b*ln(x).
3. Divide both sides by b to isolate ln(x): (y - 3) / b = ln(x).
4. Now, use the fact that the exponential function e to the power of ln(x) is x (since they are inverse functions): x = e^((y - 3) / b).

This matches option (a) from the choices provided.