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Question

If log 2 = 0 . 30103, log 3 = 0 . 4771213, log 7 = 0 . 8450980, then solve :
31+x=7x/2

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Solution

We write the given equation as (7×3)x=22x+1.(10/2)x
Taking logarithm of both side, we have
x( log 7 + log 3) = (2x + 1 ) log + 2 x(log 10 - log 2)
or x[log 7 + log 3 - 2 log 2 - log 10 + log 2] = 2
or x[log 7 + log 3 - log 2 - 1] = log 2
or x[0.8450980 + 0.4771213 - 0.3010300 - 1] = 0.03013
or x(0.0211893) = 0.30103
x = 14.207 (approx).

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