Question

ln5-lnx=-1

Answer 1

start with
\[\ln(5x)=-1\] then write in equivalent exponential form as
\[5x=e^{-1}\] or if you prefer
\[5x=\frac{1}{e}\] then divide by \(5\)

Answer 2

Alternate method \[\ln5-\ln x=-1\]
first get the x term on one side, and the other terms to the other side

\[\ln5+1=\ln x\]
now recognise \(1=\ln e\)
\[\ln5+\ln e=\ln x\]
then combine the logs
\[\ln 5e=\ln x\]
and finally raise both sides to the power e, to clear the logs
\[\]