SOLUTION: Please help me to find x and y : ln 2x + 10 = 2 ln 2

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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