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Math(alg2)

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solve the exponential equation

5(2)^2x - 4 = 13 thanks

  • Math(alg2) - ,

    If 5(2)^2x - 4 = 13 mean

    5 * [ 2 ^ ( 2 x ) ] - 4 = 13

    then

    5 * 2 ^ 2 x - 4 = 13

    5 * 2 ^ 2 x = 13 + 4

    5 * 2 ^ 2 x = 17 Divide both sides by 5

    2 ^ 2 x = 17 / 5

    2 x * log ( 2 ) = log ( 17 / 5 )

    2 x * log ( 2 ) = log ( 17 ) - log ( 5 ) Divide both sides by 2 log ( 2)

    x = [ log ( 17 ) - log ( 5 ) ] / 2 log ( 2 )



    Remark:

    log ( a / b ) = log ( a) - log ( b )

    log ( 17 / 5 ) = log ( 17 ) - log ( 5 )



    x = 0.88276737


    2 x = 1.76553474


    5 * 2 ^ 1.76553474 - 4 =

    5 * 3.4 - 4 =

    17 - 4 = 13

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