35.0k views
5 votes
Please help with 15, 17 and 19

Please help with 15, 17 and 19-example-1
User Alex Quinn
by
8.8k points

1 Answer

4 votes

Given:

15.
\log_{(1)/(2)}\left((1)/(2)\right)

17.
\log_{(3)/(4)}\left((4)/(3)\right)

19.
2^(\log_2100)

To find:

The values of the given logarithms by using the properties of logarithms.

Solution:

15. We have,


\log_{(1)/(2)}\left((1)/(2)\right)

Using property of logarithms, we get


\log_{(1)/(2)}\left((1)/(2)\right)=1
[\because \log_aa=1]

Therefore, the value of
\log_{(1)/(2)}\left((1)/(2)\right) is 1.

17. We have,


\log_{(3)/(4)}\left((4)/(3)\right)

Using properties of logarithms, we get


\log_{(3)/(4)}\left((4)/(3)\right)=-\log_{(3)/(4)}\left((3)/(4)\right)
[\because \log_a(m)/(n)=-\log_a(n)/(m)]


\log_{(3)/(4)}\left((4)/(3)\right)=-1
[\because \log_aa=1]

Therefore, the value of
\log_{(3)/(4)}\left((4)/(3)\right) is -1.

19. We have,


2^(\log_2100)

Using property of logarithms, we get


2^(\log_2100)=100
[\because a^(\log_ax)=x]

Therefore, the value of
2^(\log_2100) is 100.

User Tallulah
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories