Posted by melek on Sunday, February 19, 2012 at 7:52pm.
log ( a ^ n ) = n * log ( a )
( 2 x - 1 ) * log ( 4 ) = log ( 6 ) Divide both sides by log ( 4 )
2 x - 1 = log ( 6 ) / log ( 4 )
2 x = log ( 6 ) / log ( 4 ) + 1
2 x = log ( 6 ) / log ( 4 ) + log ( 4 ) / log ( 4 )
2 x = [ log ( 6 ) + log ( 4 ) ] / log 4
2 x = log ( 24 ) / log ( 4 ) Divide both sides by 2
x = [ log ( 24 ) / log ( 4 ) ] / 2
x = log ( 24 ) / 2 log ( 4 )
Remark:
log ( a ) + log ( b ) = log ( a * b )
log ( 4 ) + log ( 6 ) = log ( 6 * 4 ) = log ( 24 )
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