Can you solve this equation?

ln[(2x - 5)/x] = 1/4

=> (2x - 5)/x = e^1/4

so, 2x - 5 = xe^1/4

=> 2x - xe^1/4 = 5

=> x(2 - e^1/4) = 5

i.e. x = 5/(2 - e^1/4) = 6.99 (3 s.f.)

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To answer this question, you must know the properties of ln. Remember:

ln(B)+ln(A)=ln(AB)

ln(B)-ln(A)=ln(B/A)

2ln(B)=ln(B^2)

e^ln(B)=B

With these rules, we can proceed.

so ln(2x-5)-ln(x)=1/4 becomes

ln((2x-5)/x)=1/4

Then, e^(ln(2x-5)/x)=e^(1/4)

So, (2x-5)/x=e^(1/4)

2x-5=xe^(1/4)

2x=xe^(1/4)+5

2x-xe^(1/4)=5

(Remember e^(1/4) is just a number. All you have to do from here is combine the like terms of x, and divide by the resulting coefficient)

ln(2x-5) - ln(x) = 1/4

or, ln((2x-5)/x) = 1/4

or, (2x-5)/x = e^(1/4)

or, 2x - 5 = xe^(1/4)

or, x = 5/(2-e^(1/4)) = 5/(2-1.284) from calculator

or, x = 6.983