Question

solve: $ln 2x + ln 2 = 0$
$x = \boxed{}$

Explanation:

Step1: Use logarithm property

Using the property of logarithms \(\ln a+\ln b = \ln(ab)\), we can rewrite the left - hand side of the equation \(\ln 2x+\ln 2 = 0\) as \(\ln(2x\times2)=\ln(4x)\). So the equation becomes \(\ln(4x)=0\).

Step2: Convert to exponential form

Recall that if \(\ln y = k\), then \(y = e^{k}\). Since \(\ln(4x)=0\) and \(e^{0}=1\), we have \(4x = e^{0}=1\).

Step3: Solve for x

To solve for \(x\), we divide both sides of the equation \(4x = 1\) by 4. So \(x=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)