Question

If e^5x=k, where k is any positive number then what is the value of x

Answer 1

If
`k > 0`, then
`x` must be greater than 0.

Explanation:

If
`k > 0`, then we state that
`e^(5\cdot x) > 0` and
`e^(5\cdot x)` is a trascendental function with a lower bound so that
`e^(5\cdot x)> 1`. Then, the minimum value of
`k` is 1 and we proceed to solve the latter equation to find the value of
`x`:

`e^(5\cdot x)> 1`

`\ln e^(5\cdot x) > \ln 1`

`5\cdot x > 0`

`x > 0`

Therefore,
`x` must be greater than 0.