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10 May, 13:52

Exponential Form

3. log 1/4 1=0

4. log 1/2 32 = - 5

Evaluate the logarithm

6. log27 3=

8. log 1/4 256=

9. log 10.001=

10. log 64 2=

+5
Answers (2)
  1. 10 May, 14:06
    0
    6. 1/3

    8. - 4

    9. - 3

    10. 1/6
  2. 10 May, 14:12
    0
    Loga n=z ⇔a^z=n

    Therefore:

    3) log 1/4 1=0 ⇔ (1/4) ⁰=1

    4) log 1/2 32 - 5 ⇔ (1/2) ⁻⁵=2⁵=32

    6)

    log 27 3=n ⇔ 27^n=3

    27=3³

    (3³) ^n=3 ⇒n=1/3 (3³) ¹/³=3³/³=3¹=3

    Answer: log 27 3=1/3

    7)

    log1/4 256=n ⇔ (1/4) ^n=256

    256=2⁸=4⁴

    (1/4) ^n=4⁴ ⇒n=-4 [ (1/4) ⁻⁴=4⁴=256 ]

    Answer: log1/4 256=-4

    9)

    log 10 0.001=n ⇔ 10^n=0.001

    0.001=10⁻³

    10^n=10⁻³ ⇒n=-3

    answer: log 10 0.001=-3

    10)

    log 64 2=n ⇔64^n=2

    64=2⁶

    (2⁶) ^n=2 ⇒2 (⁶n) = 2¹ ⇒ 6n=1 ⇒ n=1/6

    answer: log 64 2 = 1/6
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