Question

How do you solve `e^(p+10)+4=18`?

Answer 1

`p = ln(14)-10 ~~-7.3609`

Explanation:

The base-`a` logarithm of `x`, denoted `log_a(x)`, is the power which `a` must be taken to for `a^(log_a(x))` to equal `x`. Because of this, it should be quite clear that for any `x`, we have `log_a(a^x) = x`, as `x` is the power which `a` must be taken to to obtain `a^x`.

Using this, along with the convention that the natural log `ln(x)` is the base-`e` logarithm of `x`:

`e^(p+10) + 4 = 18`

`=> e^(p+10) = 14`

`=> ln(e^(p+10)) = ln(14)`

`=> p+10 = ln(14)`

`:. p = ln(14)-10 ~~-7.3609`