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