Roboguru

Hitunglah nilai  yang memenuhi:

Hitunglah nilai begin mathsize 14px style x end style yang memenuhi:

begin mathsize 14px style square root of 9 to the power of 2 x plus 4 end exponent end root equals open parentheses 1 third close parentheses to the power of negative 3 x plus 2 end exponent end style 

Jawaban:

Dengan menggunakan konsep penyelesaian persamaan eksponen dengan basis berupa bilangan, rubahlah ruas kiri dan kanan ke basis yang sama dan gunakan sifat-sifat bilang berpangkat sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 9 to the power of 2 x plus 4 end exponent end root end cell equals cell open parentheses 1 third close parentheses to the power of negative 3 x plus 2 end exponent end cell row cell square root of open parentheses 3 squared close parentheses to the power of 2 x plus 4 end exponent end root end cell equals cell open parentheses 3 to the power of negative 1 end exponent close parentheses to the power of negative 3 x plus 2 end exponent end cell row cell square root of 3 to the power of 4 x plus 8 end exponent end root end cell equals cell 3 to the power of 3 x minus 2 end exponent end cell row cell 3 to the power of fraction numerator 4 x plus 8 over denominator 2 end fraction end exponent end cell equals cell 3 to the power of 3 x minus 2 end exponent end cell row cell 3 to the power of 2 x plus 4 end exponent end cell equals cell 3 to the power of 3 x minus 2 end exponent end cell end table end style 

Karena basis sudah sama, maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 4 end cell equals cell 3 x minus 2 end cell row cell 2 x minus 3 x end cell equals cell negative 2 minus 4 end cell row cell negative x end cell equals cell negative 6 end cell row x equals 6 row blank blank blank end table end style 

Dengan demikian nilai begin mathsize 14px style x end style yang memenuhi adalah begin mathsize 14px style x equals 6 end style.

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