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=

6. 1/3

8. - 4

9. - 3

10. 1/6

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