Tooong dibantu banget kak

Mapel : Matematika

Bab : Akar dan Pangkat
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Nomor 1]

[tex] = \frac{2 \sqrt{3} }{4 - \sqrt{8} } \times \frac{4 + \sqrt{8} }{4 + \sqrt{8} } \\ \\ = \frac{8 \sqrt{3} + 2 \sqrt{24} }{16 - 8} \\ \\ = \frac{8 \sqrt{3} + 4 \sqrt{6} }{8} \\ \\ = \sqrt{3} + \frac{1}{2} \sqrt{6} [/tex]

Opsi C


Nomor 2]

5log 3 = p
5log 7 = q


Ditanya → 45log 175√3

Penyelesaian :
___________

= 45log 175√3

= 5log 175√3 / 5log 45

= 5log [5*5*7*√3] / 5log [5*3*3]

= [2 • 5log 5 + 5log 7 + 5log 3^½] / 5log 5 + 2• 5log 3]

= 2•(1) + q + p(½) / 1 + 2•(p)

= [2 + q + p/2] / 1 + 2p

= [4/2 + 2q/2 + p/2] / [1 + 2p]

= [4 + 2q + p] /2[1 + 2p]

= [4 + 2q + p] / [2 + 4p]


Opsi C

Mapel Matematika
Bab Rasional dan Logaritma

1. 2✓3 / (4 - ✓8)

Kedua ruas kalikan dengan bilangan sekawan, 4 + ✓8
= 2✓3(4 + ✓8) / 16 - 8
= 8✓3 + 2✓24 / 8
= 8✓3 + 4✓6 / 8
= ✓3 + 1/2✓6 (C)

2.
5log3 = p
5log7 = q

45log175✓3
= 5log175✓3 / 5log45
= 5log(5x5x7x✓3) / 5log(5x3x3)
= (5log5 + 5log5 + 5log7 + 5log3^1/2) / (5log5 + 5log3 + 5log3)
= (1 + 1 + q + 1/2(p)) / (1 + p + p)
= (2 + q + (p/2)) / (1 + 2p)
= (4 + 2q + p /2) / (1 + 2p)
= (4 + 2q + p) / (2 + 4p)
(C)