To solve the equation y = e^x for x, we can take the natural logarithm (ln) of both sides. This allows us to isolate the variable x.
1. Take the natural logarithm of both sides of the equation: ln(y) = ln(e^x)
By using the logarithmic property log_b(a^c) = c * log_b(a), we can simplify ln(e^x) to just x * ln(e).
2. Simplify the equation: ln(y) = x * ln(e)
The natural logarithm of e (ln(e)) is equal to 1, so x * ln(e) simplifies to just x.
3. Rewrite the equation: ln(y) = x
Therefore, the solution to the equation y = e^x for x is x = ln(y).
In summary, to solve the equation y = e^x for x, we take the natural logarithm of both sides, which gives us x = ln(y). This means that x is equal to the natural logarithm of y