Pertanyaan

Jika ( 1 , 8 ) 10 ( 0 , 12 ) 4 ( 0 , 243 ) 6 = 5 y 2 x 3 z maka nilai dari 2 x - y +2 z = ….

Jika $\frac{( 0 , 12 ) ^{4} ( 0 , 243 ) ^{6}}{( 1 , 8 ) ^{10}} = \frac{2 ^{x} 3 ^{z}}{5 ^{y}}$ maka nilai dari 2x-y+2z=….

-24
-16
-8
1

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N. Ayu

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Jawaban terverifikasi

Pembahasan

Sehingga diperoleh x =-18, y =16 dan z =14 Nilai dari 2 x - y +2 z =2( -18) -16+2( 14) =-24

$fraction numerator left parenthesis 0 comma 12 right parenthesis to the power of 4 left parenthesis 0 comma 243 right parenthesis to the power of 6 over denominator left parenthesis 1 comma 8 right parenthesis to the power of 10 end fraction equals fraction numerator 2 to the power of x 3 to the power of z over denominator 5 to the power of y end fraction fraction numerator left parenthesis 12 cross times 10 to the power of negative 2 end exponent right parenthesis to the power of 4 left parenthesis 243 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 6 over denominator left parenthesis 18 cross times 10 to the power of negative 1 end exponent right parenthesis to the power of 10 end fraction equals fraction numerator begin display style 2 to the power of x 3 to the power of z end style over denominator begin display style 5 to the power of y end style end fraction fraction numerator left parenthesis 3 cross times 4 cross times 10 to the power of negative 2 end exponent right parenthesis to the power of 4 left parenthesis 3 to the power of 5 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 6 over denominator left parenthesis 2 cross times 9 cross times 10 to the power of negative 1 end exponent right parenthesis to the power of 1 0 end fraction equals fraction numerator begin display style 2 to the power of x 3 to the power of z end style over denominator begin display style 5 to the power of y end style end fraction fraction numerator left parenthesis 3 cross times 2 squared cross times 10 to the power of negative 2 end exponent right parenthesis to the power of 4 left parenthesis 3 to the power of 5 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 6 over denominator left parenthesis 2 cross times 3 squared cross times 10 to the power of negative 1 end exponent right parenthesis to the power of 1 0 end fraction equals fraction numerator begin display style 2 to the power of x 3 to the power of z end style over denominator begin display style 5 to the power of y end style end fraction fraction numerator 3 to the power of 4 cross times 2 to the power of 8 cross times 10 to the power of negative 8 end exponent cross times 3 cubed 0 cross times 10 to the power of negative 18 end exponent over denominator 2 to the power of 10 cross times 3 to the power of 20 cross times 10 to the power of negative 10 end exponent end fraction equals fraction numerator begin display style 2 to the power of x 3 to the power of z end style over denominator begin display style 5 to the power of y end style end fraction 3 to the power of 4 plus 30 minus 20 end exponent cross times 2 to the power of 8 minus 10 end exponent cross times 10 to the power of negative 8 minus 18 plus 10 end exponent equals fraction numerator begin display style 2 to the power of x 3 to the power of z end style over denominator begin display style 5 to the power of y end style end fraction 3 to the power of 14 cross times 2 to the power of negative 2 end exponent cross times 10 to the power of negative 16 end exponent equals fraction numerator begin display style 2 to the power of x 3 to the power of z end style over denominator begin display style 5 to the power of y end style end fraction$

Sehingga diperoleh x=-18, y=16 dan z=14

Nilai dari 2x-y+2z=2(-18)-16+2(14)=-24