soal logaritma dan sifat-sifatnya

September 01, 2020

Contoh Latihan Soal Logaritma

Contoh Soal 1

²log 16 =….

Pembahasan:
$^{2}log 16=^{2}log2^{4}$
$=4.^{2}log2$
$=4.1$
$=4$

Contoh Soal 2

$^{5}log100-^{5}log4=...$
Pembasahan :
$^{5}log100-^{5}log4=^{5}log\frac{100}{4}$
$=^{5}log25$
$=^{5}log5^{2}$
$=2.^{5}log5$
$=2.1$
$=2$

Contoh Soal 3

$^{2}log3.^{3}log4.^{4}log2=...$
Pembahasan :
$^{2}log3.^{3}log4.^{4}log2=^{2}log2$
$=1$

Contoh Soal 4

Jika ³log 2 = a, maka ³log 6 =….

Pembahasan :

$^{3}log6=^{3}log (2\times 3)$
$=^{3}log2+^{3}log3$
$=a+1$

2 log 25 . 5 log 4 + 2 log 6 – 2log 3
9 log 36 / 3 log 7
9^(3 log 7)

Jawab :

a. 2 log 25 . 5 log 4 + 2 log 6 – 2log 3

= 2 log 52 . 5 log 22 + 2 log (3.2/3)
= 2.2 . 2 log 5 . 5 log 2+ 2 log 2
= 2 . 2 log 2 + 1
= 2 . 1 + 1
= 3

b. 9 log 4 / 3 log 7

= 3^2 log 22 / 3 log 7
= 3 log 2 / 3 log 7
= 7 log 2

c. 9^(3 log 7)

= 32 ^(3 log 7)
= 3^(2 .3 log 7)
= 3^(3 log 49)
= 49

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