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
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
To solve the equation ln(sqrt(x-8)) = 5, you need to follow a few steps. Let's go through it:
Step 1: Remove the square root from both sides of the equation. To do this, you can square both sides of the equation:
(ln(sqrt(x-8)))^2 = 5^2
This simplifies to:
ln(x-8) = 25
It is perfectly fine to square both sides of the equation.
Step 2: Note that ln(x-8) = 25. Now, you need to convert the logarithmic equation into an exponential equation. Recall that ln(x) = y is equivalent to e^y = x. Applying this to our equation, we get:
e^25 = (x-8)
Step 3: Add 8 to both sides of the equation:
e^25 + 8 = x
Therefore, the solution to the equation ln(sqrt(x-8)) = 5 is x = e^25 + 8.
The answer you provided, x = 8 + e^10, may be incorrect. Make sure to double-check your calculations and steps to see if any errors were made.