Question

2 ln x = ln(5 + 4x)

Answer 1

\[2 \ln x =\ln(5+4x)\]
\[\ln x ^{2}=\ln (5+4x)\]
\[e ^{\ln x ^{2}}=e ^{\ln(5+4x)}\]
\[x ^{2}=5+4x\]
\[x ^{2}-4x-5=0\]
\[(x-5)(x+1)=0\]
\[x=5\]
\[x=-1\]

Answer 2

There's a law of logarithms that says
\[\large n*\ln(x) = \ln(x^{n})\]

there's also one that says if
\[\ln(a)=\ln(b)\]then
\[a=b\]