Question

log base 5 (3) - log base 5 (5x) = 2

Answer 1

2 log_4 5x = 3
log_4 5x = 3/2
5x = 4^(3/2)
5x = 8
x = 8/5

Answer 2

quotient law states that when log_a (b) - log_a (c) = log_a (b/c)

since in this one you have the same bases...you can do it like that

log_5 (3/5x) = 2

we need to isolate x..so we will change it to exponential form so the x will go on one side and all non-x will go on the other

5^2 = 3/5x

25 = 3/5x

crossmultiply...

25(5x) = 3(1)

125x = 3
---- ---
125 125

x = 3/125

Answer 3

x = 3/125

Answer 4

log5(3)-log5(5x)=2
log5(3/5x)=log5(5^2)
3/5x=5^2
3=25*5x
3=125x
x=3/125

Answer 5

\[\log_{5}3 - \log_{5}5x =2 \]By\[\log a - \log b = \log (a/b)\]You'll get\[\log_{5}(3 /5x) =2 \]Since 2 = (2log5)/(log5^2)/(log5) \[\log_{5}(3 /5x) =log_{5}5^2 \]As they have the same base, you can 'cancel' it and rewrite it as \[3/(5x)= 5^2\]This gives you 3 = (5)(5)(5x)
3= 125x
Divide both sides by 125 and you'll get the answer