Question

Solve In(5x + 3) = 2.5​

Answer 1

`x=(e^(2.5)-3)/(5)`

Explanation:

Let y = 5x + 3
Then we get
㏑(y) = 2.5

Using exponentiation,

`e^(lny) = e^(2.5)\\\textrm{But }e^(lny) \textrm{ is simply y (log rule)}\\\textrm{So we get}\\y = e^(2.5)\\\\\\\textrm{Substituting for y we get}\\\\5x + 3 = e^(2.5)\\x = (e^(2.5) - 3)/5\\`

This works out to x = 1.83649879