anonymous
  • anonymous
log base 5 (3) - log base 5 (5x) = 2
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
2 log_4 5x = 3 log_4 5x = 3/2 5x = 4^(3/2) 5x = 8 x = 8/5
lgbasallote
  • lgbasallote
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
anonymous
  • anonymous
x = 3/125

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jhonyy9
  • jhonyy9
log5(3)-log5(5x)=2 log5(3/5x)=log5(5^2) 3/5x=5^2 3=25*5x 3=125x x=3/125
Callisto
  • Callisto
\[\log_{5}3 - \log_{5}5x =2 \]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

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