Question

Kuis:
Cari nilai x jika
[tex]^2log(x^2-2)\:=\:^{(x^2-2)}log2[/tex]

Answer 1

Penjelasan dengan langkah-langkah:

LogAritma

^2 log(x²-2) = ^(x²-2) log2

^2 log(x²-2) = ^2 log2/^2 log(x²-2)

^2 log(x²-2)(^2 log(x²-2)) = ^2 log2

^2 log(x²-2)² = ^2 log2

^2 log(x²-2)² = 1

^2 log(x²-2) = √1

^2 log(x²-2) = ±1

...untuk ^2 log(x²-2) = -1 → x²-2 = 2^-1

x²-2 = ½

x² = ½+2

x² = ½5

x = ±√½5

x = ±(√5/√2 × √2/√2)

x = ±½√10

...untuk ^2 log(x²-2) = 1 → x²-2 = 2^1

x²-2 = 2

x² = 2+2

x² = 4

x = √4

x = ±2

.

maka nilai x = {-2 , -½√10 , ½√10 , 2}

Answer 2

PEMBAHASAN

[tex] \displaystyle \sf ^{2}log \: ( {x}^{2} - 2) = \ ^{ {x}^{2} - 2}log \: 2 \\ \\ \displaystyle \sf \: {(log \: 2)}^{2} = \: {(log \: ( {x}^{2} - 2))}^{2} [/tex]

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(log (x² - 2))² - (log 2)² = 0

(log (x² - 2) + log 2)(log (x² - 2) - log 2)) = 0

(log 2(x² - 2)) (log (x² - 2)/2) = 0

log 2(x² - 2) = 0

2(x² - 2) = 1

x² - 2 = 1/2

x² = 5/2

x = - √(5/2) = - 1/2 √10 atau x = √(5/2) = 1/2 √10

log (x² - 2)/2 = 0

(x² - 2)/2 = 1

x² - 2 = 2

x² = 4

x = -2 atau x = 2

Nilai x yang memenuhi ada 4 :

-2 , -1/2 √10 , 1/2 √10 , dan 2