2. Write the following expressions as log N and find their values. (1) log 2 + log 5 (11) log, 16 - log, 2 (ui) 3 logga 4 (iv) 2 log 3 - 3 log 2 log 10+ 2 log 3 – log 2 (V)
Answers
Step-by-step explanation:
Given :-
(i) log 2 + log 5
(ii) log, 16 - log 2
(iii) 3 log 4
(iv) 2 log 3 - 3 log 2
(v) log 10+ 2 log 3 – log 2
To find :-
Write the following expressions as log N and find their values?
Solution:-
i) Given that log 2 + log 5
We know that
log ab = log a + log b
=> log (2×5) = log N
=> log 10 = log N
=> N = 10
Therefore, N = 10
ii) Given that
log 16 -log 2
We know that
log a/b = log a - log b
=> log (16/2) = log N
=> log 8 = log N
=> N = 8
Therefore, N = 8
iii) Given that 3 log 4
We know that
log a^m = m log a
=> log 4³ = log N
=> log 64 = log N
=> N = 64
Therefore, N = 64
iv) Given that
2 log 3 - 3 log 2
We know that
log a^m = m log a
=> log 3² - log 2³
=> log 9 - log 8
We know that
log a/b = log a - log b
=> log 9/8 = log N
=> N = 9/8
Therefore, N = 9/8
v) Given that
log 10+ 2 log 3 – log 2
We know that
log a^m = m log a
=> log 10 + log 3² - log 2
=> log 10 + log 9 - log 2
We know that
log ab = log a + log b
=> log (10×9)-log 2
=> log 90- log 2
We know that
log a/b = log a - log b
=> log (90/2) = log N
=> log 45 = log N
=> N = 45
Therefore, N = 45
Answer:-
I) N = 10
ii) N = 8
iii) N = 64
iv) N = 9/8
v) N = 45
Used formulae:-
→ log ab = log a + log b
→ log a/b = log a - log b
→ log a^m = m log a