Jika ^2loga-2(^2logb)= 2 dan ^2logb + 2(^2loga) = -1,maka nilai ab adalah .... Question from @firmanbjw

whongaliem $^{2}log 2a$ - 2 . $^{2}log b$ = 2
$^{2}log a$ - $^{2}log b^{2}$ = $^{2} log 4$
$^{2} log \frac{a}{ b^{2} }$ = $^{2}log 4$
$\frac{a}{ b^{2} }$ = 4 ---> a = 4.b² .... pers i
$^{2}log b$ + 2 . $^{2}log a$ = - 1
$^{2}log b$ + $^{2} log a^{2}$ = $^{2} log \frac{1}{2}$
$^{2} log \frac{b}{ a^{2} }$ = $^{2} log \frac{1}{2}$
$\frac{b}{ a^{2} }$ = $\frac{1}{2}$
b = $\frac{1}{2}$ .a² ---- subtitusikan pada pers i
a = 4 . $(\frac{1}{2} a^{2}) ^{2}$
a = 4 . $\frac{1}{4}$ . $a^{4}$
1 = $a^{3}$
a = ∛1
a = 1 -----> b = $\frac{1}{2}$ .a²
b = $\frac{1}{2}$ .1²
b = $\frac{1}{2}$
a .b = 1 . $\frac{1}{2}$
= $\frac{1}{2}$

0 votes Thanks 2

Ridafahmi ²log a - 2 ²log b = 2
²log a - ²log b² = ²log 2²
²log ( $\frac{a}{ b^{2} }$ ) = ²log 4
      $\frac{a}{b ^{2} } =4$
   a = 4b² persamaan I

²log b + 2 ²log a = -1
²log b + ²log a² = ²log $2^{-1}$
   ²log (b×a²) = ²log 1/2
   ba² = 1/2
      2ba² = 1 persamaan II

2b (4b²)² = 1
2b 16b⁴ = 1
   32 b⁵ = 1
   $b^{5} = \frac{1}{32} \\ b= \sqrt[5]{( \frac{1}{ 2 } ) ^{5} } \\ b= \frac{1}{2}$
subtitusikan
a = 4b²
a = 4 (1/2)²
   = 4 × 1/4
a = 1

nilai ab = 1 × 1/2
   = 1/2

0 votes Thanks 1

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