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