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Persamaan eksponen melalui titik  adalah...

Pertanyaan

Persamaan eksponen melalui titik left parenthesis 1 comma 6 right parenthesis space dan space left parenthesis 2 comma 24 right parenthesis adalah...space 

Pembahasan Soal:

Untuk mengetahui persamaan eksponen yang melalui titik left parenthesis 1 comma 6 right parenthesis space dan space left parenthesis 2 comma 24 right parenthesis, maka perlu diawali dari bentuk umum dari persamaan eksponen tersebut, perhatikan penghitungan berikut!

 y equals b. a to the power of x space dengan space a comma space b space adalah space bilangan space real  untuk space titik space left parenthesis 1 comma 6 right parenthesis 6 equals b. a to the power of 1 6 equals a b... left parenthesis straight i right parenthesis  untuk space titik space left parenthesis 2 comma 24 right parenthesis 24 equals b. a squared 24 equals a squared b... left parenthesis ii right parenthesis  Eliminasi space pers. left parenthesis straight i right parenthesis space dan space left parenthesis ii right parenthesis bottom enclose a squared b equals 24 a b space space equals 6 space space space space space minus end enclose a squared minus a equals 18 a squared minus a minus 18 equals 0 a subscript 1 comma 2 end subscript equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction a subscript 1 comma 2 end subscript equals fraction numerator negative open parentheses negative 1 close parentheses plus-or-minus square root of open parentheses negative 1 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses negative 18 close parentheses end root over denominator 2 open parentheses 1 close parentheses end fraction a subscript 1 comma 2 end subscript equals fraction numerator 1 plus-or-minus square root of 1 plus 72 end root over denominator 2 end fraction a subscript 1 comma 2 end subscript equals fraction numerator 1 plus-or-minus square root of 73 over denominator 2 end fraction a subscript 1 equals fraction numerator 1 plus square root of 73 over denominator 2 end fraction a subscript 2 equals fraction numerator 1 minus square root of 73 over denominator 2 end fraction substitusi space nilai space a space ke space pers. space left parenthesis straight i right parenthesis a b equals 6 left right arrow b equals 6 over a untuk space a equals fraction numerator 1 plus square root of 73 over denominator 2 end fraction b equals fraction numerator 6 over denominator fraction numerator 1 plus square root of 73 over denominator 2 end fraction end fraction b equals fraction numerator 12 over denominator 1 plus square root of 73 end fraction b equals fraction numerator 12 over denominator 1 plus square root of 73 end fraction cross times fraction numerator 1 minus square root of 73 over denominator 1 minus square root of 73 end fraction b equals fraction numerator 12 open parentheses 1 minus square root of 73 close parentheses over denominator 1 squared minus open parentheses square root of 73 close parentheses squared end fraction b equals fraction numerator 12 open parentheses 1 minus square root of 73 close parentheses over denominator 1 minus 73 end fraction b equals fraction numerator 12 open parentheses 1 minus square root of 73 close parentheses over denominator negative 72 end fraction b equals negative fraction numerator 1 open parentheses 1 minus square root of 73 close parentheses over denominator 6 end fraction sehingga comma space y equals negative fraction numerator 1 open parentheses 1 minus square root of 73 close parentheses over denominator 6 end fraction open parentheses fraction numerator 1 plus square root of 73 over denominator 2 end fraction close parentheses to the power of x  untuk space a equals fraction numerator 1 minus square root of 73 over denominator 2 end fraction b equals fraction numerator 6 over denominator fraction numerator 1 minus square root of 73 over denominator 2 end fraction end fraction b equals fraction numerator 12 over denominator 1 minus square root of 73 end fraction b equals fraction numerator 12 over denominator 1 minus square root of 73 end fraction cross times fraction numerator 1 plus square root of 73 over denominator 1 plus square root of 73 end fraction b equals fraction numerator 12 open parentheses 1 plus square root of 73 close parentheses over denominator 1 squared minus open parentheses square root of 73 close parentheses squared end fraction b equals fraction numerator 12 open parentheses 1 plus square root of 73 close parentheses over denominator 1 minus 73 end fraction b equals fraction numerator 12 open parentheses 1 plus square root of 73 close parentheses over denominator negative 72 end fraction b equals negative fraction numerator 1 open parentheses 1 plus square root of 73 close parentheses over denominator 6 end fraction sehingga comma space y equals negative fraction numerator 1 open parentheses 1 plus square root of 73 close parentheses over denominator 6 end fraction open parentheses fraction numerator 1 minus square root of 73 over denominator 2 end fraction close parentheses to the power of x  Catatan colon open parentheses a minus b close parentheses open parentheses a plus b close parentheses equals a squared minus b squared open parentheses 1 plus square root of 73 close parentheses open parentheses 1 minus square root of 73 close parentheses equals 1 squared minus open parentheses square root of 73 close parentheses squared equals negative 72     

Jadi, persamaan eksponen yang melalui titik left parenthesis 1 comma 6 right parenthesis space dan space left parenthesis 2 comma 24 right parenthesis adalah y equals negative fraction numerator open parentheses 1 minus square root of 73 close parentheses over denominator 6 end fraction open parentheses fraction numerator 1 plus square root of 73 over denominator 2 end fraction close parentheses to the power of x atau y equals negative fraction numerator open parentheses 1 plus square root of 73 close parentheses over denominator 6 end fraction open parentheses fraction numerator 1 minus square root of 73 over denominator 2 end fraction close parentheses to the power of x. 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Mei 2021

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