Question 1135343
32^(2y) = 5^(4y+1)
:
(32^2)^y = (5^(4)^y) * 5
:
1024^y = 625^y * 5
:
take ln (natural log) of both sides of =
:
yln(1024) = yln(625) +ln(5)
:
Note ln(a^b) = bln(a) and ln(ab) = ln(a) + ln(b)
:
yln(1024) - yln(625) = ln(5)
:
y(ln(1024) - ln(625)) = ln(5)
:
yln(1024/625) = ln(5)
:
Note ln(a) - ln(b) = ln(a/b)
:
y = ln(5)/ln(1024/625)
:
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y = 3.2598
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