How do you solve #e^(3x)=5#?

Question

13051 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-19T07:12:03

Use properties of logarithms to find that #x = ln(5)/3#

We will be using the following properties of logarithms:

Now, using the standard notation of the natural logarithm #ln(x)# to denote #log_e(x)# we have:

#e^(3x) = 5#

#=> ln(e^(3x)) = ln(5)#

#=> 3xln(e) = ln(5)#

#=> 3x*1 = ln(5)#

#=>3x = ln(5)#

#:. x = ln(5)/3#