How do you solve 10 = e ^ x?

3 Answers
Dec 15, 2015

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).

Dec 15, 2015

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

Dec 15, 2015

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