2log3 + 3log2 + log5 - log 12
Answers
Step-by-step explanation:
log9+log8+log5-log12
log(9×8×5÷12)
log30
1.47
Step-by-step explanation:
Given:-
2log3 + 3log2 + log5 - log 12
To find:-
Write the given logarithmic expression in one term
Solution:-
Method-1:-
Given that
2log3 + 3log2 + log5 - log 12
=>2 log 3 + 3 log 2 + log 5 - log (2×2×3)
=> 2 log 3 + 3 log 2 + log 5 - log (2^2×3)
We know that
log a× loa b = log ab
=>2 log 3 + 3log 2 + log 5 -( log 2^2+log3)
We know that
log a^m = m log a
=>2 log 3 + 3 log 2 + log 5 -(2log2 + log 3)
=>2 log 3+ 3 log 2 + log 5 - 2 log 2 - log 3
=>(2log3 -log3)+(3 log2-2log2)+log 5
=>(2-1) log 3 + (3-2) log 2 + log 5
=>log 3 + log 2 + log 5
we know that
log a× loa b = log ab
=>log (3×2×5)
=>log 30
Method-2:-
Given that
2log3 + 3log2 + log5 - log 12
We know that
log a^m = m log a
=>log 3^2 + log 2^3 + log 5 - log 12
=>log 9 + log 8 + log 5 - log 12
we know that
log a× loa b = log ab
=>log (9×8×5) - log 12
=>log 360 - log 12
we know that
log (a / b) = log a - log b
=>log (360/12)
=>log 30
(or)
1.4771...
Answer:-
The single term of the logarithmic form of the given logarithmic expression is
log 30 (or) 1.4771...
Used formulae:-
- log a× loa b = log ab
- log (a / b) = log a - log b
- log a^m = m log a