Logaritma Phytong
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Latihan Logaritma 3 log 5 + 2 log − 2 log 3 5 12. 2 =……. 4 log 2i log 5i 2 log16
1. 3 log 9 =
2
2. 4 log 32 = 25
3. 5
log3
1 2 3 log + 4 log 2 9 =…… 13. 3 25 log 2i log 3i 2 log 5
=
4. 3 log 42 + 3 log12 − 3 log 56 =
4
×
(
)
9
log 2
= …….
5. Jika log 8 = m tentukan : a. log 2
14. 2
b. 4 log 3
15. ( 2 log 9 + 8 log 3)( 3 log 2 + 9 log 4 ) =……
6. Jika a log x = p ; a log y = q ; a log z = r
( 16.
3
9
Tentukan : a. a log
x3 z y2
17.
3
log 5
27
log 45 ) − ( 3 log15) 2
2
3 + 2i 3 log 5
(
)
(
=…….
)
log x y + log y x − log ( xy ) log ( xy )
=…
2
b. x log y z 7. Diketahui 3 log 2 = m dan 7 log 3 = n Berapa : 12 log 42 = ….. 8. 3 log 45i 5 log 75 − ( 3 log 25 + 5 log 9 ) =……
18. Diketahui 5 log 2 = a ; 4 log 3 = b 72 log 225 =……… 19. 3 log ( x + 2 ) + 3 log ( x − 4 ) = 3 , x=…… 20. Buktikan
9. Diketahui 120 log 3 = a ; 120 log 2 = b
1 ⎛ x +1⎞ log x 2 − 1 + ilog ⎜ ⎟ = log ( x + 1) 2 ⎝ x −1 ⎠
3 log 25 + 5 log 4 =………
21. Buktikan
10. 5 log ( 4 log ( 2 log16 ) ) = ……. 11. 8 log ( 9 log ( 2 log 8) ) =……..
log z i y log z = x log z + y log z x
22. log 30 − 48
1 + log10
23. 3 3 log 27 × ( 3 )
9
16
xy
log z
1 =…….. log10
log 625
=……..
( 24.
6
log 9 3
) −( 2
6
( 25.
5
6
log 4 2
3 log 3 8
log x ) − ( 5 log y ) 2
5
)
32.
2
=…..
1 2
log 20 log 3 5 − 1 4 log 9 + −2 + log 3. 9 log16 − log 2 5 2 log10 log 5 − 1
2
log x − 5 log y
=…….
33. Diketahui 3 log 5 = x ; 5 log 7 = y 2
26. Diketahui 5 log 3 = a ; 2 log 25 = b
hitunglah 35 log 75 3 =…..
Hitung: 15 log 20
34. Diketahui 2 log 3 = a ; 3 log 7 = b hitunglah 42 log 56 =…
27. Jika 5 log ( 9 x − 4 ) = 2 , x =……..
1 6
35. a log 3 625 − a log 125 + = o , nilai a
28. 2
16 1 + 18 − 7 log 7 3 ⎡ log 3 3 ⎤ 9 log 2 :⎢6 − log 2 ⎥ 3 4 6 log 4i log 6i log 9 ⎣ log 3 ⎦
log
36.Buktikan 1 p
1
1 3.log 24 =….. 29. log 3 3 log 6 + log 20 − log 5
30. ( 2 log 3)
5
1 −1 log + 5 log 2 + 3 log ( ab ) + 3 log ( ab ) 2
p 1 q log r + q log r s log . log p. log r = p q log s + q log s
⎛
37. ⎜ a ⎝
1 b
log c
⎞ ⎟ ⎠
c
⎛1⎞ log ⎜ ⎟. a log b ⎝d⎠
=……..
38. 106log x − 4 (103log x ) = 12 , x =……..
=…
1 1 + log 9 − log 625 27 =… 1 log 4 + log 25 3 3
2.log
31.
1 1 2 2 1 39. 4 log x = − . 4 log ( a + b ) + ⎡⎢ 4 log ( a − b ) − 4 log ( a + b ) + .log ( 2b ) − 4 log ( 2a ) ⎤⎥ 4⎣
2
Bukitkan x = 4
⎡ log 20 − log 50 ⎤ 40. ⎢ ⎥ ⎣ log 2 − log 5 ⎦ 2
2
3
( a − b ) 3 4.b2 2 2 3 ( a + b ) . 2a ( a + b ) (
2
)
log5 + 3 log5 . 6 log 5 5 2
log5. 3 log5
=…….
3
2
⎦
1. 3 log 9 =
2
2. 4 log 32 = 25
3. 5
log3
1 2 3 log + 4 log 2 9 =…… 13. 3 25 log 2i log 3i 2 log 5
=
4. 3 log 42 + 3 log12 − 3 log 56 =
4
×
(
)
9
log 2
= …….
5. Jika log 8 = m tentukan : a. log 2
14. 2
b. 4 log 3
15. ( 2 log 9 + 8 log 3)( 3 log 2 + 9 log 4 ) =……
6. Jika a log x = p ; a log y = q ; a log z = r
( 16.
3
9
Tentukan : a. a log
x3 z y2
17.
3
log 5
27
log 45 ) − ( 3 log15) 2
2
3 + 2i 3 log 5
(
)
(
=…….
)
log x y + log y x − log ( xy ) log ( xy )
=…
2
b. x log y z 7. Diketahui 3 log 2 = m dan 7 log 3 = n Berapa : 12 log 42 = ….. 8. 3 log 45i 5 log 75 − ( 3 log 25 + 5 log 9 ) =……
18. Diketahui 5 log 2 = a ; 4 log 3 = b 72 log 225 =……… 19. 3 log ( x + 2 ) + 3 log ( x − 4 ) = 3 , x=…… 20. Buktikan
9. Diketahui 120 log 3 = a ; 120 log 2 = b
1 ⎛ x +1⎞ log x 2 − 1 + ilog ⎜ ⎟ = log ( x + 1) 2 ⎝ x −1 ⎠
3 log 25 + 5 log 4 =………
21. Buktikan
10. 5 log ( 4 log ( 2 log16 ) ) = ……. 11. 8 log ( 9 log ( 2 log 8) ) =……..
log z i y log z = x log z + y log z x
22. log 30 − 48
1 + log10
23. 3 3 log 27 × ( 3 )
9
16
xy
log z
1 =…….. log10
log 625
=……..
( 24.
6
log 9 3
) −( 2
6
( 25.
5
6
log 4 2
3 log 3 8
log x ) − ( 5 log y ) 2
5
)
32.
2
=…..
1 2
log 20 log 3 5 − 1 4 log 9 + −2 + log 3. 9 log16 − log 2 5 2 log10 log 5 − 1
2
log x − 5 log y
=…….
33. Diketahui 3 log 5 = x ; 5 log 7 = y 2
26. Diketahui 5 log 3 = a ; 2 log 25 = b
hitunglah 35 log 75 3 =…..
Hitung: 15 log 20
34. Diketahui 2 log 3 = a ; 3 log 7 = b hitunglah 42 log 56 =…
27. Jika 5 log ( 9 x − 4 ) = 2 , x =……..
1 6
35. a log 3 625 − a log 125 + = o , nilai a
28. 2
16 1 + 18 − 7 log 7 3 ⎡ log 3 3 ⎤ 9 log 2 :⎢6 − log 2 ⎥ 3 4 6 log 4i log 6i log 9 ⎣ log 3 ⎦
log
36.Buktikan 1 p
1
1 3.log 24 =….. 29. log 3 3 log 6 + log 20 − log 5
30. ( 2 log 3)
5
1 −1 log + 5 log 2 + 3 log ( ab ) + 3 log ( ab ) 2
p 1 q log r + q log r s log . log p. log r = p q log s + q log s
⎛
37. ⎜ a ⎝
1 b
log c
⎞ ⎟ ⎠
c
⎛1⎞ log ⎜ ⎟. a log b ⎝d⎠
=……..
38. 106log x − 4 (103log x ) = 12 , x =……..
=…
1 1 + log 9 − log 625 27 =… 1 log 4 + log 25 3 3
2.log
31.
1 1 2 2 1 39. 4 log x = − . 4 log ( a + b ) + ⎡⎢ 4 log ( a − b ) − 4 log ( a + b ) + .log ( 2b ) − 4 log ( 2a ) ⎤⎥ 4⎣
2
Bukitkan x = 4
⎡ log 20 − log 50 ⎤ 40. ⎢ ⎥ ⎣ log 2 − log 5 ⎦ 2
2
3
( a − b ) 3 4.b2 2 2 3 ( a + b ) . 2a ( a + b ) (
2
)
log5 + 3 log5 . 6 log 5 5 2
log5. 3 log5
=…….
3
2
⎦
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