# Question #db5cd

##### 1 Answer

Feb 10, 2017

#### Explanation:

Use

#1/e = 2e^(3x - 4)#

Cross multiply:

#1 = 2e^(3x - 4)e^1#

Use

#1 = 2e^(3x - 4 + 1)#

#1 = 2e^(3x - 3)#

#1/2 = e^(3x - 3)#

Take the natural logarithm of *both* sides.

#ln(1/2) = ln(e^(3x- 3))#

Use

#ln(1/2) = (3x- 3)lne#

#ln(1/2) = 3x- 3#

#1/3(ln(1/2) + 3) = x#

Use

#1/3(ln1 - ln2 + 3) = x#

We know that

#1/3(3 - ln2) = x#

#1 - 1/3ln2 = x#

Use

#1 - ln2^(1/3) = x#

#1 - lnroot(3)(2) = x#

Hopefully this helps!