Tolong pake caranya kak. terima kasih

Tolong pake caranya kak. terima kasih

Jawab:

$displaystyle frac{3^{n+12}times9^{2n-7}}{3^{5n}}=frac{3^{n+12}times(3^2)^{2n-7}}{3^{5n}}\frac{3^{n+12}times9^{2n-7}}{3^{5n}}=frac{3^{n+12}times3^{2(2n-7)}}{3^{5n}}\frac{3^{n+12}times9^{2n-7}}{3^{5n}}=3^{n+12+4n-14-5n}\frac{3^{n+12}times9^{2n-7}}{3^{5n}}=3^{-2}\frac{3^{n+12}times9^{2n-7}}{3^{5n}}=frac1{3^{2}}\frac{3^{n+12}times9^{2n-7}}{3^{5n}}=frac1{9}$

$displaystylefrac{12}{sqrt6+sqrt2}=frac{12}{sqrt6+sqrt2}cdotfrac{sqrt6-sqrt2}{sqrt6-sqrt2}\frac{12}{sqrt6+sqrt2}=frac{12(sqrt6-sqrt2)}{(sqrt6)^2-(sqrt2)^2}\frac{12}{sqrt6+sqrt2}=frac{12(sqrt6-sqrt2)}{6-2}\frac{12}{sqrt6+sqrt2}=frac{12(sqrt6-sqrt2)}{4}\frac{12}{sqrt6+sqrt2}=3(sqrt6-sqrt2)$

$displaystylelog_42+log_24+log_93+log_39=frac12+2+frac12+2\log_42+log_24+log_93+log_39=5$

Beberapa konsep yang dipakai:

$displaystyletriangleright~(a^b)^c=a^{bc}\triangleright~a^btimes a^c=a^{b+c}\triangleright~frac{a^b}{a^c}=a^{b-c}\triangleright~a^{-b}=frac1{a^b}\triangleright~(a+b)(a-b)=a^2-b^2\triangleright~a^b=cLeftrightarrow log_ac=b~;~a,c>0text{ dan }aneq1$

Jawab:

Penjelasan dengan langkah-langkah:

aᵇ x aⁿ = aᵇ⁺ⁿ

aᵇ + aⁿ = aᵇ⁻ⁿ

$frac{3^{n+12}times9^{2n-7} }{3^{5n} } =frac{3^{n+12}times(3^{2})^{2n-7} }{3^{5n} }\ \=frac{3^{n+12}times3^{4n-14}}{3^{5n} }\ \=3^{n+12+4n-14-5n}\\=3^{-2} \\=frac{1}{3^{2} } \\=frac{1}{9} \$

opsi pilihan ( c )

$frac{12}{sqrt{6}+sqrt{2} } \\=frac{12}{sqrt{6} +sqrt{2} } timesfrac{sqrt{6}-sqrt{2}}{sqrt{6} -sqrt{2} }\ \=frac{12(sqrt{6} -sqrt{2}) }{6-2}\ \=frac{12(sqrt{6} -sqrt{12} }{4} \\=3(sqrt{6} -sqrt{2})$

opsi pilihan ( d )

ᵃlog b + ᵃlog b = ᵃlog ( bc)

ᵃlog b = ᵃⁿlog bⁿ

ᵃlog aᵇ = b

⁴log 2 + ²log 4 + ⁹log 3 + ³log 9

= ⁴log 2 + ⁴log 4² + ⁹log 3 + ⁹log 9²

= ⁴log ( 2 x 16 ) + ⁹log ( 3 x 81 )

= ⁴log 32 + ⁹log 243

= ⁴log 2⁵ + ⁹log 3⁵

= ²log 2⁵/² + ³log 3⁵/²

= 5/2 + 5/2

= 10/2

= 5

opsi pilihan tidak ada

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