Question

How do you solve `e^lnx=12`?

Answer 1

`x=12`

Explanation:

`color(red)(ln(x))` means `color(red)(" the value "k" you need as an exponent of e for " e^k" to be equal to x")`

Therefore
`color(white)("XXX")color(blue)(e)^color(red)(ln(x))`
means
`color(white)("XXX")color(blue)(e)` raised to the exponent of `color(red)(" the value "k" you need as an exponent of e for " e^k" to be equal to x")`

While this is a bit of a mind twister, if you think it though, what this means is that
`color(white)("XXX")e^(ln(x))=x`