2014-10-17T20:56:58+05:30
Log(729/3x)=4 Taking antilog at both sides We have 243/x=10000 x= 243/10000= .0243
NO NOT LIKE THAT
3X+4 IS UP TO LOG
Put it under bracket then!!
2014-10-18T00:22:39+05:30

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It is not clear if the 4 is with in logarithm or outside :
if the question is Log (3x+4) = Log 729   =>   3x+4 = 729    x = 725/3
Otherwise see below:

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Let us assume that given logarithms are with respect to 10.

Log 3 x + 4 = Log 729 = Log 9³  = Log 3⁶

(Log 3 + Log x) + 4 = 6 Log 3

Log x = 5 Log 3 - 4  = Log 3⁵ - 4 Log 10 = Log 243 - Log 10⁴ = Log (243 /10,000)

Removing the logarithms,   x = 243/10,000 = 0.0243
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Alternately,

Log 3x + 4 = Log 729
Log 3x = Log 729 - 4 = Log 729/10,000
3x = 729/10,000
x = 243/10,000