Pertanyaan

Jika diketahui 2 lo g a + 2 lo g b = 12 d an 3 2 l og a − 3 2 l o g b = 4 , maka a + b adalah ....

Jika diketahui $^{2} lo g a +^{2} lo g b = 12 d an 3^{2} l og a - 3^{2} l o g b = 4$ , maka a + b adalah ....

144
272
528
1024
1040

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

$rightwards arrow squared log space a space plus space squared log space b space equals space 12 space squared log space a space plus space squared log space b space equals space squared log 12 space L o g space a plus space L o g space b space equals L o g space a b squared L o g a space x space b space equals to the power of 2 space end exponent L o g 12 a b equals space 2 to the power of 12 b equals 2 to the power of 12 over a...........1 right parenthesis rightwards arrow 3 squared l og space a space minus space 3 squared l o g space b space equals space 4 a space L o g space b space equals L o g space a to the power of b L o g space a space minus space L o g space b space equals space L o g space a over b 3 squared space L o g space a space minus to the power of space 2 end exponent space L o g space b space equals space 4 squared space L o g space a cubed space minus space squared space L o g space b space equals squared space L o g space 2 to the power of 4 squared log a cubed over b equals squared space L o g space 2 to the power of 4 a cubed over b equals 2 to the power of 4...........2 right parenthesis P e r s a m a a n space 1 space d i s u b s t i t u s i space k e space p e r s a m a a n space 2 a cubed over b equals 2 to the power of 4 fraction numerator a to the power of 13 over denominator begin display style 2 to the power of 12 over a end style end fraction equals 2 to the power of 4 a cubed equals open parentheses 2 to the power of 4 close parentheses open parentheses 2 to the power of 16 over a close parentheses a to the power of 4 equals 2 to the power of 16 a equals 2 to the power of 4 m a k a space b equals 2 to the power of 12 over a equals 2 to the power of 12 over 2 to the power of 4 equals 2 to the power of 8 a space plus space b space equals space 16 space plus space 256 space equals space 272$