Math, asked by abdulsattar98490, 2 months ago

2log3 + 3log2 + log5 - log 12

Answers

Answered by shahfaizmanzoor597
1

Step-by-step explanation:

log9+log8+log5-log12

log(9×8×5÷12)

log30

1.47

Answered by tennetiraj86
1

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
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