Jika 4y+3x=64 dan xlog(x+12)−3xlog4=−1, maka x + 2y = ...

Pertanyaan

Jika $\style{font-size:14px}{4^{\mathrm y+3\mathrm x}=64\;\mathrm{dan}\;^{\mathrm x}\log\left(\mathrm x+12\right)-3^{\mathrm x}\log4=-1,}$ maka x + 2y = ...

86
36
-5
-14
-34

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style rightwards double arrow 4 to the power of straight y plus 3 straight x end exponent equals 64 left right double arrow 4 to the power of straight y plus 3 straight x end exponent equals 4 cubed left right double arrow straight y plus 3 straight x equals 3... left parenthesis straight i right parenthesis rightwards double arrow to the power of straight x log left parenthesis straight x plus 12 right parenthesis minus 3 to the power of straight x log 4 equals negative 1 blank to the power of straight x log left parenthesis straight x plus 12 right parenthesis minus to the power of straight x log 4 cubed equals negative 1 to the power of straight x log fraction numerator left parenthesis straight x plus 12 right parenthesis over denominator 4 cubed end fraction equals negative 1 fraction numerator left parenthesis straight x plus 12 right parenthesis over denominator 4 cubed end fraction equals straight x to the power of negative 1 end exponent fraction numerator left parenthesis straight x plus 12 right parenthesis over denominator 4 cubed end fraction equals straight x to the power of negative 1 end exponent fraction numerator left parenthesis straight x plus 12 right parenthesis over denominator 64 end fraction equals 1 over straight x straight x left parenthesis straight x plus 12 right parenthesis equals 64 straight x squared plus 12 straight x equals 64 straight x squared plus 12 straight x minus 64 equals 0 open parentheses straight x plus 16 close parentheses open parentheses straight x minus 4 close parentheses equals 0 straight x equals negative 16 space atau space straight x equals 4 end style$

Substitusikan x = 4 ke persamaan (i) :
y+3x = 3 <=> y + 3(4) = 3
y + 12 = 3 <=> y = - 9
Hasil dari x + 2y = 4 + 2(- 9) = 4 - 18 = -14