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