Question

what is the solution to 2 ln x = 4 ln 2?
x =
done

Explanation:

Step1: Simplify using logarithm property

Recall the logarithm power rule: \(a\ln b=\ln(b^a)\). Apply it to both sides:
\(2\ln x = \ln(x^2)\) and \(4\ln 2=\ln(2^4)\). So the equation becomes \(\ln(x^2)=\ln(16)\).

Step2: Use one - to - one property of ln

If \(\ln a=\ln b\), then \(a = b\) (for \(a,b>0\)). Thus, \(x^2 = 16\).

Step3: Solve for x

Take square roots: \(x=\pm4\). But for \(\ln x\) to be defined, \(x>0\). So \(x = 4\).

Answer:

\(4\)