Question

if sqrt(a-b) = (b/a)^(1-2x)
then find the value of x

Answer 1

Solve for x:
sqrt(a-b) = (b/a)^(1-2 x)
Reverse the equality in sqrt(a-b) = (b/a)^(1-2 x) in order to isolate x to the left hand side.
sqrt(a-b) = (b/a)^(1-2 x) is equivalent to (b/a)^(1-2 x) = sqrt(a-b):
(b/a)^(1-2 x) = sqrt(a-b)
Taking reciporicals of both sides lets us solve for x in the numerator.
Take reciporicals of both sides:
(a (b/a)^(2 x))/b = 1/sqrt(a-b)
Divide both sides by a constant to simplify the equation.
Divide both sides by a/b:
(b/a)^(2 x) = b/(a sqrt(a-b))
Eliminate the exponential from the left hand side.
Take the logarithm base b/a of both sides:
2 x = (log(b/(a sqrt(a-b))))/(log(b/a))+((2 i) pi n)/(log(b/a)) for n element Z
Solve for x.
Divide both sides by 2:
Answer: |
| x = (log(b/(a sqrt(a-b))))/(2 log(b/a))+(i pi n)/(log(b/a)) for n element Z

Answer 2

can it be shown in a simplified form so dat i can undrstnd? u might like to use "equation"(symbols) in order to clarify