Question

How do you solve `10 = e ^ x`?

Answer 1

`x = ln(10)`

Explanation:

To get rid of the base `e`, we can take the natural log of both sides:

`10 = e^x -> ln(10) = ln(e^x) -> x = ln(10)`

This value is irrational, so the only exact way to write it is `ln(10)`.

Answer 2

I found: `x=2.3025`

Explanation:

One way is to take the natural log of both sides (which can be evaluated using a pocket calculator) to get:
`ln10=lne^x`
where from the definition of log:
`lne^x=x`
so:
`x=ln10=2.3025`

Answer 3

Take the natural log of both sides of the equation ...

Explanation:

`ln10=ln(e^x)`

Now, simplify and solve for x ...

`ln10=x`

`x~~2.3026`

Verify ...

`e^2.3026=10.000`

hope that helped