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solve 6^(3n) = 43^(5n-4)?
explain please
a) 1.1202
b) -1.9005
c) -0.2800
d) 2.1418
take the log of both sides and use the rule log A^p = p log A:
(3n) log 6 = (5n-4) log 43
multiply out:
3n log 6 = 5n log 43 - 4 log 43
rearrange to factor n out:
5n log 43 - 3n log 6 = 4 log 43
n (5 log 43 - 3 log 6) = 4 log 43
divide both sides:
n = 4 log 43 / (5 log 43 - 3 log 6)
put into calculator and you get:
a) 1.1202
that's it! 
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