# How do you solve #4ln(5x)+5=2#?

##### 2 Answers

#### Explanation:

In order to solve this, we will begin with removing 5 from both sides:

Thus, we will get

Then we will divide both sides by 4 to get

Then, to get x alone, we need to recognize the relationship of

Remember that

Thus, continuing:

Divide both sides by 5 and we will get

If you plug this into the equation for x, you will get

#### Explanation:

Isolate the logarithm and then cancel it out by raising everything to a common base.

First, subtract 5 from both sides.

#4ln(5x)+5-5=2-5#

#4ln(5x)+cancel5-cancel5=2-5#

#4ln(5x) = -3#

Next, divide both sides by 4.

#4ln(5x) div 4 = -3 div 4#

#cancel4ln(5x) div cancel4 = -3 div 4#

#ln(5x) = -3/4#

Next, raise

#e^ln(5x) = e^(-3/4)#

#cancele^(cancel"ln"(5x))=e^(-3/4)#

#5x = e^(-3/4)#

And finally divide by 5.

#5x div 5 = e^(-3/4)div5#

#cancel5x div cancel5 = e^(-3/4)/5#

#x = e^(-3/4)/5#

*Final Answer*