How do i solve 5^x=3^(x+6)
[From: ] [author: ] [Date: 11-07-04] [Hit: ]
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How do I solve 5^x=3^(x+6)?
Sol Take ln both side
x(ln 5) = (x+6)(ln 3)
x(ln 5) - x ln (3) = 6 (ln 3)
x{ln 5 - ln 3} = 6*(ln 3)
x{1.6094379124341 - 1.0986122886681} = 6*{1.0986122886681}
x* {0.510825623766} = 6.5916737320086
x = 6.5916737320086/ 0.510825623766
= 12.9039606185223918696................An…
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use logarithms. Some scientific calculators make that really easy. If you know what a logarithm is, it should be pretty easy. Sorry, but I'm not going to give you the answer.
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Go to myalgebra.com
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Take logs of both sides
x log(5) = (x + 6)log(3)
x(log(5) – log(3)) = 6log(3)
x = 6log(3)/(log(5) – log(3))
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xlog5 = (x+6)log3
xlog5 = xlog3 +6log3
xlog5 - xlog3 = 6log 3
x = 6log3/(log5-log3)
