Question 888691: Please help me to find x and y : ln 2x + 10 = 2 ln 2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! ln(2x) + 10 = 2ln(2)
subtract 10 from both sides of the equation to get:
ln(2x) = 2ln(2) - 10
since 2ln(2) is equal to ln(2^2) = ln(4), your equation becomes:
ln(2x) = ln(4) - 10
simplify to get:
ln(2x) = -8.613705639
this is true if and only if e^-8.613705639 = 2x
divide both sides of this equation by 2 to get:
x = e^-8.613705639 / 2 which becomes:
x = 9.079985952 * 10^-5.
that should be your answer.
replace x in the original equation with that to see if the equation holds true.
original equation is:
ln(2x) + 10 = 2ln(2) which becomes:
ln(2*9.079985952 * 10^-5) + 10 = 2ln(2) which becomes:
1.386294361 = 1.386294361
this confirms the solution is correct.
i did not see a y in your equation.
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