Pertanyaan

Jika 3 lo g 4 = a + 1 , maka 8 lo g 9 = ...

Jika $^{3} lo g 4 = a + 1$ , maka $^{8} lo g 9 = ...$

$begin mathsize 14px style fraction numerator 1 over denominator a plus 1 end fraction end style$
a+ 1
$begin mathsize 14px style fraction numerator a plus 1 over denominator 2 end fraction end style$
$begin mathsize 14px style fraction numerator a plus 1 over denominator 3 end fraction end style$

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Pembahasan

Ingat, Bentuk umum logaritma! sifat-sifat Logaritma: Maka: Maka: Sehingga:

Ingat, Bentuk umum logaritma!

sifat-sifat Logaritma:

$begin mathsize 14px style straight a right parenthesis straight space to the power of straight a log straight space 1 equals 0 straight b right parenthesis straight space to the power of straight a log invisible function application straight b equals fraction numerator 1 over denominator straight space to the power of straight b log invisible function application straight a end fraction straight c right parenthesis space to the power of straight a log invisible function application straight b plus straight space to the power of straight a log invisible function application straight c equals straight space to the power of straight a log invisible function application open parentheses straight b. straight c close parentheses straight d right parenthesis straight space to the power of straight a log invisible function application straight b minus straight space to the power of straight a log invisible function application straight c equals straight space to the power of straight a log invisible function application open parentheses straight b over straight c close parentheses end style$

Maka:

$begin mathsize 14px style log invisible function application 3 straight a minus fraction numerator 1 over denominator straight space to the power of 6 straight a squared end exponent log invisible function application 10 end fraction plus fraction numerator 1 over denominator straight space to the power of 2 straight a end exponent log invisible function application 10 end fraction equals straight space to the power of 10 log invisible function application 3 straight a minus straight space to the power of 10 log invisible function application 6 straight a squared plus straight space to the power of 10 log invisible function application 2 straight a space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight space to the power of 10 log invisible function application open parentheses fraction numerator 3 straight a.2 straight a over denominator 6 straight a squared end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight space to the power of 10 log invisible function application open parentheses fraction numerator 6 straight a squared over denominator 6 straight a squared end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight space to the power of 10 log invisible function application 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0 end style$

Maka:

$begin mathsize 14px style 2. space cubed log invisible function application 2 equals a plus 1 space cubed log invisible function application 2 equals fraction numerator a plus 1 over denominator 2 end fraction end style$

Sehingga:

$space to the power of 8 log invisible function application 9 equals space to the power of 2 cubed end exponent log invisible function application 3 squared equals 2 over 3. space squared log invisible function application 3 equals 2 over 3. fraction numerator 1 over denominator space cubed log invisible function application 2 end fraction equals 2 over 3. fraction numerator a plus 1 over denominator 2 end fraction equals fraction numerator a plus 1 over denominator 3 end fraction subscript blank$