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