Natural Log Rules

What is the reason that

y=\ln(9)-\ln(x)+\ln(4)

comes out as

y=\frac{\ln(36)}{\ln(x)}

instead of

y=\frac{\ln(9)}{\ln(4x)}

Reply 1

TeeEm

Original post by Jimmy_M

What is the reason that

y=\ln(9)-\ln(x)+\ln(4)

comes out as

y=\frac{\ln(36)}{\ln(x)}

instead of

y=\frac{\ln(9)}{\ln(4x)}

what?

Reply 2

Jimmy_M

Original post by TeeEm

what?

Okay probably not explained very well..
I'm wondering why

y=\ln(9)-\ln(x)+\ln(4)

simplifies into

y=\frac{\ln(36)}{\ln(x)}

when the original equation could be

y=\ln(9)-(\ln(x)+\ln(4))

, in which case surely the simplification would be

y=\frac{\ln(9)}{\ln(4x)}

Reply 3

TeeEm

Original post by Jimmy_M

Okay probably not explained very well..
I'm wondering why

y=\ln(9)-\ln(x)+\ln(4)

simplifies into

y=\frac{\ln(36)}{\ln(x)}

when the original equation could be

y=\ln(9)-(\ln(x)+\ln(4))

, in which case surely the simplification would be

y=\frac{\ln(9)}{\ln(4x)}

firstly
the "could be" could NOT be

secondly
both expressions you give are wrong
the correct answer is ln(36/x)

Reply 4

Jimmy_M

Original post by TeeEm

firstly
the "could be" could NOT be

secondly
both expressions you give are wrong
the correct answer is ln(36/x)

Sorry yeah that's what I meant, stupid mistake there.. I also realised that

-\ln(x)

is actually just

\ln(x)^{-1} = \ln(\frac{1}{x})

Silly question really :biggrin:

Reply 5

TeeEm

Original post by Jimmy_M

Sorry yeah that's what I meant, stupid mistake there.. I also realised that

-\ln(x)

is actually just

\ln(x)^{-1} = \ln(\frac{1}{x})

Silly question really :biggrin:

no worries

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