Question

Solve for x in the equation ln(2x – 1) – ln(x -1) = ln 5.

Answer 1

you would have to know that
\[\ln A -\ln B = \ln \frac { A }{ B }\]

Answer 2

so using that you get
\[\ln \frac{ 2x-1 }{ x-1 } = \ln 5\]

Answer 3

NICE PRACTICE @kausarsalley

Answer 4

so now using the definition of log, which says
\[\log _ba=x\] is the same as writing
\[b ^{x}=a\]

Answer 5

sorry for the late reply......having problems

Answer 6

\[\frac{ 2x-1 }{ x-1 }=e ^{\ln 5}\]

Answer 7

can you continue from there???
or should i further explain??

Answer 8

Can you explain more?

Answer 9

\[2x-1=e ^{\ln 5}(x-1)\]
\[2x-1=e ^{\ln 5}x-e ^{\ln5}\]

Answer 10

\[e ^{\ln 5}x-2x=e ^{\ln 5}-1\]
\[5x-2x=5-1\]
\[3x=4\]
\[x=\frac{ 4 }{ 3 }\]

Answer 11

@sfb