Can I multiply e to ln to cancel ln?

For example, I want to cancel 2ln on both sides of the equation': 2ln(√x+1)=2ln(√y+1) by multiplying all to 1/2 e. Is that correct?

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  • Alan
    Lv 7
    1 month ago
    Favourite answer

    No, if you want to get rid of the ln  

    You raise e^() of both sides 

    e^(2(ln( sqrt(x) +1)  = e^(2*ln (sqrt(y) + 1)) 

    e^(ln  ( (sqrt(x) + 1)^2 ) =   e^(ln ( sqrt(Y) +1)^2 ) 

    (sqrt(x) + 1)^2  = (sqrt(y) + 1) ^2 

    or you could multiply both side by 1/2 first

    then raise to e^() of both sides  

    e^(ln( sqrt(x) + 1)  ) = e^(ln(sqrt(y) + 1)  

    sqrt(x) + 1 = sqrt(y) +1    

    sqrt(x) =sqrt(y)   x> 0 , y> 0 

    square both sides 

    x = y     for x> 0  and y >0  

  • 1 month ago

    You cannot. There is no meaning in writing elnx = x. Because "ln" is a function. Not a number.

  • 1 month ago

    (√x+1) = e^(ln(√x+1))

    ln(...) is a function that produces a unique value.

    So, it's like you have f(√x+1) = f(√y+1)

    where f(...) is a 1 to 1 function 

    in which case, you can conclude that

    (√x+1) = (√x+1)

  • 1 month ago

    2ln(√x+1)=2ln(√y+1)

    First remove the coefficient '2' to become the index number. 

    Hence 

    2ln(√x+1)=2ln(√y+1)

    Then Antilog.

    (√x+1)^2=(√y+1)^2 

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  • 1 month ago

    If you double the logarithm of a number, it becomes the logarithm of the SQUARE of the number.  That is, if, say k = ln(z), then 2k = ln(z^2).

    Apply that to your equation

    2ln(√x+1)=2ln(√y+1)

    to re-write it as 

    ln(√x+1)^2 = ln(√y+1)^2

    and if the logarithms are equal, then the numbers must be equal, that is

    (√x+1)^2 = (√y+1)^2

    Is that what you are looking for?

    (Of course, this obviously means that x = y).

  • 1 month ago

    requires a reverse logarithm, which is an exponent.  you need to use e^x to get rid of the ln x.  e^(lnx) actually.  need both sides to have the same change to maintain the equality, of course, and I am sure you already knew that.

    So, you might change a problem of lnx on one side into an e^x (or some other variable) on the other.

  • david
    Lv 7
    1 month ago

    NO.  ln is an operation -- like multiplication. division, addition, and subtraction are math operations.... 

     . . .e  on the other hand is a number .. not an operation

    just like pi is a number (approx. 3.14159)  e is also an irrational number approx 2.71828 = = = ln is NOT a number but an operation preformed on on a number ===  ln (4)  =  1.38629 (approx)  = = =you are not multiplying by ln

  • Dixon
    Lv 7
    1 month ago

    Yes, you can get rid of the 2's by dividing by 2 (multiplying by half). Then you get ln operating on the whole of both sides. Mathematically you remove logs by "taking logs" but here just by reason, if it operates on the whole of each side and they are equal then they must have been the same before the operator was applied, so you can just remove it. In fact by inspection you can just look at the whole of

    2ln(√x + 1) = 2ln(√y + 1)

    and see by symmetry that to be equal, then x = y, with some cavitats about ±

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