You need to simplify using the logarithmic identities such that:

You need to simplify using the logarithmic identities such that:

You need to solve for x the equation such that:

**Hence, evaluating the solution to the given equation yields **

You need to solve for x the equation such that:

Hence, evaluating the solution to the given equation yields

i) ln(2x) + ln(2/x)

We know that:

ln a + ln b = ln a*b

==> ln (2x)*(2/x) = **ln 4**

ii) ln(x^2 - 1)- ln(x-1)

We know that:

ln a - ln b = ln (1/b)

==> ln (x^2-1)/(x-1) = **ln (x+1)**

i) lnx = 5

**==> x= e^5**

ii) lnx + ln5 = ln10

==> ln 5*x = ln 10

==> 5x = 10

==>** x= 2**

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