How do you solve $5^(5y-2)=2^(2y+1)$ ?

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Answer 1 · 2016-10-16T13:30:26

$5^(5y - 2) = 2^(2y + 1)$

$ln(5^(5y - 2)) = ln(2^(2y + 1))$

$(5y - 2)ln5 = (2y + 1)ln2$

$5yln5 - 2ln5 = 2yln2 + ln2$

$5yln5 - 2yln2 = ln2 + 2ln5$

$y(5ln5 - 2ln2) = ln2 + 2ln5$

Apply the rules $alnn = lnn^a$ , $lna - lab = ln(a/b)$ and $lna + lnb = ln(a xx b)$ to simplify.

$y(ln781.25) = ln50$

$y = ln50/ln781.25$

$y = 0.59$

Hopefully this helps!

How do you solve 5^(5y-2)=2^(2y+1)5^(5y-2)=2^(2y+1)?