Pre-calc Solve logarithmic

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ln sqrt(x-8)= 5

I would like help to solve this what i did was to take away the square root i squared both sides coming up with

(ln sqrt(x-8))^2= (5)^2

ln(x-8)=25

am i alowed to do this with ln in the equation?

then i subtract 8 from both sides

ln x = 17

e^(ln x)= e^17
e cancels out ln leaving with
x=e^17

this is not right the real answer is
x = 8 + e^10 on math-way but how?

thanks

  • Pre-calc Solve logarithmic -

    Not even close.

    ln√(x-8) = 5
    1/2 ln(x-8) = 5
    ln(x-8) = 10
    x-8 = e^10
    x = 8+e^10

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