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Mathematics 29 Online
OpenStudy (anonymous):

log subscript 6 x + log subscript 6 (x-5)=2

OpenStudy (lgbasallote):

your lesson is really funny =)) \[\log_6 x + \log_6 (x-5) = 2\] do you know laws of logarithms

OpenStudy (anonymous):

no i actually never took this math before thats the problem

OpenStudy (lgbasallote):

the product law of logarithms states that: \[\Large \log_a b + \log_a c = \log_a (bc)\] do you get the application?

OpenStudy (lgbasallote):

i mean how you can apply the law on this problem?

OpenStudy (anonymous):

by getting the logs of the two 6's and combining them thus creating (bc ?? 0_0

OpenStudy (lgbasallote):

yup..the question is..what is bc in this case?

OpenStudy (anonymous):

0.778?? and for the x-5 would u use the natural log

OpenStudy (lgbasallote):

what didyou do?

OpenStudy (anonymous):

i took the log of 6?

OpenStudy (lgbasallote):

hmm not quite..

OpenStudy (lgbasallote):

let's try this again \[\LARGE \log_6 x + \log_6 (x+5)\] doyou agree that this is in the form \[\huge \log_a b + \log_a c\]

OpenStudy (anonymous):

yes

OpenStudy (lgbasallote):

what's a in \[\large \log_6 x + \log_6 (x+5)\]

OpenStudy (anonymous):

x

OpenStudy (lgbasallote):

nope look carefullywhere a is placed in \[\huge \log_a b + \log_a c\]

OpenStudy (anonymous):

6?

OpenStudy (lgbasallote):

yes 6. what is b?

OpenStudy (anonymous):

x

OpenStudy (lgbasallote):

and c?

OpenStudy (anonymous):

0?

OpenStudy (lgbasallote):

nope.. look carefully at \[\huge \log_6 x + \log_6 (x+5)\] and compare it with \[\huge \log_a b + \log_a c\] hint: we already decided a = 6 and b = x

OpenStudy (anonymous):

5

OpenStudy (lgbasallote):

nope.. let's try to substitute a and b into 6 and x respectively \[\huge \log_a b + \log_a c = \log_6 x + \log_6 c\] what is that c supposed to be?

OpenStudy (anonymous):

:( idk

OpenStudy (lgbasallote):

notice the difference here...\ \[\Huge \log_6 x + \log_6 c \rightarrow \log_6 x + \log_6 (x-5)\]

OpenStudy (lgbasallote):

what can yo say?

OpenStudy (anonymous):

idk

OpenStudy (lgbasallote):

what do you see as difference?

OpenStudy (lgbasallote):

spot the difference..

OpenStudy (jiteshmeghwal9):

If the base are same then the following property is used; i.e\[\log_{a}{b}+\log_{a}{c}=\log_{a}{bc} \] now, use this property to the question as follows \[\log_{6}{x} +\log_{6}{x-5}=2=>\log_{6}{x^2-5x}=2 \] now change it into exponential form as\[6^2=x^2-5x\] \[=>36=x^2-5x]/ \[=>x^2-5x-36=0\] now solve this quadratic equation & get ur answer.

OpenStudy (jiteshmeghwal9):

understood @sharee2012

OpenStudy (anonymous):

no

OpenStudy (jiteshmeghwal9):

then, why did u give me medal???

OpenStudy (anonymous):

-_-

OpenStudy (anonymous):

-4?

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