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justaguide eNotes educator| Certified Educator

We have to solve the equation: 2*ln x - 4*ln 11 = 0

We know that n*log a = log a^n

2*ln x - 4*ln 11 = 0

=> ln x - 2*ln 11 = 0

=> ln x = 2*ln 11

=> ln x = ln 11^2

taking the antilog of both the sides

x = 11^2 = 121

The required value of x is 121

giorgiana1976 | Student

We'll move the number alone to the right side:

2lnx = 4ln11

We'll use the power property of logarithms:

ln x^2 = ln 11^4

Since the bases are matching, we'll use the one to one property of logarithms:

x^2 = 11^4

We'll take square root both sides:

x1 = sqrt 11^4

x1 = 11^2

x1 = 121

x2 = -121

Since the solution of the equation has to be positive for the logarithms to exist, we'll accept as a solution only x = 121.

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