Simplify: i) ln(2x) + ln(2/x) ii) ln(x^2 - 1)- ln(x-1) Then solve: i) lnx = 5 ii) lnx + ln5 = ln10 Simplify: i) ln(2x) + ln(2/x) ii) ln(x^2 - 1)- ln(x-1) Then solve: i) lnx = 5 ii) lnx + ln5 = ln10

Expert Answers

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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

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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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