10 SOAL LOGARITMA

Soal :

1. Tentukan bentuk sederhana dari 2 log 3 + 4 log 3

2. Hitunglah nilai dari log 4ଶ . log 2ସ + log 4ଶ

3. Jika log 3ଶ = , log 2ହ = , tentukan log 30ଵ

4. Tentukan nilai dari log 24ଷ − log 8ଷ + log 9ଷ

5. Jika log= dan log= maka tentukan nilai logଷଶ

6. Diketahui 3ଶା௫ = 45, maka tentukan nilai dari 3ଶ௫

7. Tentukan nilai dari log 8 . log 9ଶ . logଵ

ସଽ

ଶ

8. Hitung nilai dari log( log 125)ହ − log( log 27ଽ . log 49 )ଷଷ

9. Jika log 5 = 2 , hitunglah nilai dari log 32ହ

10. Hitunglah nilai dari୪୭మସ�ାమ � ୪୭ଷ�.ర ୪୭ଵవ �ା�ଶ ୪୭ସ�.య ୪୭ଶభల

ହ ୪୭ଵఱ �ା� ୪୭షభଶହమ

Jawab :

1. 2 log 3 + 4 log 3 = log 3ଶ + log 3ସ = log 9 + log 81 = log 9 . 81 = log 729

2. log 4ଶ . log 2ସ + log 4ଶ = log 2ଶ + log 2ଶଶ = 1 + 2 = 3

3. log 3ଶ =

log 2ହ =

log 5ଶ =1

maka log 30ଵ =୪୭ଷమ

୪୭ଵమ =୪୭ହ.ଷ.ଶమ

୪୭ଷ.ଷ.ଶమ =୪୭ହమ �ା� ୪୭ଷమ �ା� ୪୭ଶమ

୪୭ଷమ �ା� ୪୭ଷ�ା�మ ୪୭ଶమ =భ

�ା��ା�ଵ

�ା��ା�ଵ=

ଵାା

ଶା

4. log 24ଷ − log 8ଷ + log 9ଷ = log 8 . 3ଷ − log8ଷ + log 3ଶଷ

= log 8ଷ + log 3ଷ − log8ଷ + 2 log 3ଷ

= log 3ଷ + 2 log 3ଷ = 1 + 2 = 3

5. log= log= logଷଶ = logଷ + logଶ = 3 log+ 2 log= 2+ 3

6. 3ଶା௫ = 45 3ଶ . 3௫ = 3ଶ . 5 3௫ = 5 log 5 = ଷݔ

Maka

2 log 5 = ଷݔ2

log 5ଶ = ଷݔ2

log 25 = ଷݔ2

3ଶ௫ = 25

7. log 8 . log 9ଶ . logଵ

ସଽ

ଶ = log 2ଷ . log 3ଶଶ . logଵ

మ=

ଷ��.��ଶ

ଷ

ଷయ . logଵ

మ

= 2 . −2= −4

8. log( log 125)ହ − log൫ log 27ଽ . log 49 ൯ଷଷ

= log( log 5ଷ)ହ − logቀ log 3ଷଷమ . log 7ଶ ቁଷଷ

= log 3 − log൬1

2. 3 . 2൰ଷଷ

= 1 − 1= 0

9. log 5 = 2 ୪୭ହ

୪୭= 2

୪୭ହ

୪୭ଶయ= 2

୪୭ହ

ଷ�୪୭ଶ= 2

୭ହ

୪୭ଶ= 3 . 2

log 5ଶ = 6

Maka log 32ହ = log 2ହ = 5 log 2ହ = 5ଵ

୪୭ହమ = 5 .ଵ

ହ =ହ

10.୪୭మସ�ାమ � ୪୭ଷ�.ర ୪୭ଵవ �ା�ଶ ୪୭ସ�.య ୪୭ଶభల

ହ ୪୭ଵఱ �ା� ୪୭షభଶହమ =( ୪୭ସ)మ మ�ା� ୪୭ଷ�.ర ୪୭ସమయమ �ା�ଶ ୪୭ସ�.య ୪୭ଷయరమ

ଵ�ା( ୪୭ଶఴ)మ

=ସ�ା�

భ

మ.��ଶ� ୪୭ସర �ା�ଶ�.

భ

మ.��ଷ ୪୭ଷయ

ଵ� �

=ସାଵାଷ

ଵ

=

= 1