1. log2 1024=log2 2^10=10log2 2=10·1=10
2. log3 (1/27)=log3 3^-3=-3log3 3=-3·1=-3
3. log16 2=log2^4 2=1/4 log2 2=1/4·1=1/4
4. log√2 16=log2^1/2 (2^4)=1/(1/2)log2 2^4=2·4log2 2=8·1=8
5. log5 (1/625)=log5 5^-4=-4log5 5=-4·1=-4
6. log8 1=0 , bo 8^0=1
7. log64 (1/2)=log2^6 (2^-1)=1/6log2 (2^-1)=1/6·(-1)log2 2=-1/6·1=-1/6
8. log1/4 16=log4^-1 (4^2)=-1log4 (4^2)=-1·2log4 4=-2·1=-2
9. log√2 4=log2^1/2 (2^2)=2log2 (2^2)=2·2log2 2=4·1=4
10. log7 (1/49)=log7 7^-2=-2log7 7=-2·1=-2
11. log100000=log10^5=5log10=5·1=5
12. log(1/100)=log 10^-2=-2log10=-2·1=-2
13. log5 (25^1/5)=log5 (5^2)^1/5=1/5log5 (5^2)=1/5·2log5 5=2/5log5 5=2/5·1=2/5
Korzystaliśmy z wzorów:
a) log a a=1 , dla a∈(0,1)∪(1,∞)
b) loga b^n=nloga b , dla b > 0 ∧ a∈(0,1)∪(1,∞)
c) loga^n b=1/nloga b
