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

LHS: because alnx = lnx^a, 2ln2x = ln(2x)² = ln4x²

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

e^{ln4x^2} = e^{1 + ln3}

4x² = e^{1 + ln3}

x² = (e^{1 + ln3}) / 4

x = sq root of [(e^{1 + ln3}) / 4]

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