Solve log7 (x – 8) – log7 3 = log7 21

Question

anonymous · Answer

Try to show you work :)
Whenever you stop i will help ..

anonymous · Answer

ok

anonymous · Answer

x-8/3=21

anonymous · Answer

Nope.
Show your work step by step to see which part is hard ?

anonymous · Answer

no this is where im stuck at

anonymous · Answer

hmm,Actually thats wrong and that mean that the previous step which lead to this was wrong..

anonymous · Answer

Btw : here is hint
$$Logx=Logy$$
x=y

anonymous · Answer

well all i did was put log7(x-8)over log7(3)=log7 21
then just took off the log7

anonymous · Answer

Its not $$ \Large \frac{Log_{7}(x-8)}{Log_{7}(3)}$$
It is :
$$ \Large Log_{7} \frac{(x-8)}{(3)}$$

anonymous · Answer

So now u have 
$$ \Large \frac{x-8}{3}=21$$
63=x-8
x=71

anonymous · Answer

ok but were did you get 63

anonymous · Answer

ooh neverminod i got it thanks

anonymous · Answer

21*3

anonymous · Answer

lets look over some basic properties such as log(a/b) = log a - log b and log(a*b)= log a + log b  and if logx= log y then x=y

just because everything is in the base of 7 we could use these properties as well so therefore from your question 

log7 (x – 8) – log7 3 = log7 21 let us use the first property on the left side and get log7((x-8)/3) = log 7 21and now let us use the third property  to obtain (x-8)/3 = 21

and that will get us x-8 = 63 and now solve for x to obtain x = 71 :)

anonymous · Answer

thanks for the help everyone.I really needed it