Solve the equation 2ln2x = 1 + ln3. Give your answer correct to 2dp.

LHS: because alnx = lnxa, 2ln2x = ln(2x)2 = ln4x2

Now, because ln and e are inverse functions, we take both sides to the power of e. Therefore:

eln4x^2 = e1 + ln3

4x2 = e1 + ln3

x2 = (e1 + ln3) / 4

x = sq root of [(e1 + ln3) / 4]

entering into the calculator, this gives us +/- 1.43

Answered by Shiv S. Maths tutor

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