SOLUTION: Please help me with this problem: ln(4)-ln(x)=10

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Question 194916: Please help me with this problem: ln(4)-ln(x)=10
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
ln%284%29-ln%28x%29=10 Start with the given equation


ln%284%2Fx%29=10 Combine the logs using the identity ln%28x%29-ln%28y%29=ln%28x%2Fy%29


e%5E10=4%2Fx Use the property ln%28x%29=y ----> e%5Ey=x to rewrite the equation.


x%2Ae%5E10=4 Multiply both sides by "x"


x=4%2Fe%5E%2810%29 Divide both sides by e%5E%2810%29


So the solution is x=4%2Fe%5E%2810%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

First thing to remember is that the difference of the logs is the log of the quotient, i.e.



So:



Next thing:



So:



Which is the exact answer. A little calculator work gets you to a numerical approximation.



John