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Posted by on Sunday, February 19, 2012 at 7:52pm.

Find the solution of the exponential equation, correct to four decimal places.

4^(2x − 1) = 6

  • pre-cal - , Sunday, February 19, 2012 at 10:54pm

    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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