Question

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

Answer 1

your lesson is really funny =))

\[\log_6 x + \log_6 (x-5) = 2\]
do you know laws of logarithms

Answer 2

no i actually never took this math before thats the problem

Answer 3

the product law of logarithms states that:

\[\Large \log_a b + \log_a c = \log_a (bc)\]
do you get the application?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

what didyou do?

Answer 9

i took the log of 6?

Answer 10

hmm not quite..

Answer 11

let's try this again

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

Answer 12

yes

Answer 13

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

Answer 14

x

Answer 15

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

Answer 16

6?

Answer 17

yes 6. what is b?

Answer 18

x

Answer 19

and c?

Answer 20

0?

Answer 21

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

Answer 22

5

Answer 23

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?

Answer 24

:( idk

Answer 25

notice the difference here...\

\[\Huge \log_6 x + \log_6 c \rightarrow \log_6 x + \log_6 (x-5)\]

Answer 26

what can yo say?

Answer 27

idk

Answer 28

what do you see as difference?

Answer 29

spot the difference..

Answer 30

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.

Answer 31

understood @sharee2012

Answer 32

no

Answer 33

then, why did u give me medal???

Answer 34

-_-

Answer 35

-4?