Question

How do you solve `ln sqrt(x-8)= 5`?

Answer 1

We go step by step un-doing the things that are being done to the variable, `x`, making sure that we do the same thing to both sides arriving at the answer:

`x=e^10+8`

Explanation:

We go step by step un-doing the things that are being done to the variable, `x`, making sure that we do the same thing to both sides. The first thing we encounter is the natural logarithm, which we can un-do using it's inverse, `e^x`. Starting with the left hand side:

`e^ln(sqrt(x-8))=sqrt(x-8)`

then the right hand side is:

`e^5`

Which makes our equation:

`sqrt(x-8)=e^5`

Now we un-do the square-root by squaring both sides. Starting with the left hand side:

`(sqrt(x-8))^2=x-8`

and the right hand side:

`(e^5)^2=e^(5*2)=e^10`

which makes our equation:

`x-8=e^10`

Now we can add `8` to both sides giving:

`x=e^10+8`