Question

please answer fast please​

Answer 1

Answer:

log 3600

Step-by-step explanation:

2log3+3log5+5log2

We know that, logx  

y

=ylogx,

Using the above property we can reduce the given equation as,

=log3  

2

+log5  

3

+log2  

5

 

=log9+log125+log32

also, logx+logy+logz=logxyz, hence we can write the above as,

=log(9×125×32)

=log(36000)

∴    2log3+3log5+5log2 can be written as a single logarithm as log36000.

Answer 2

Step-by-step explanation:

Given:-

2 log 3 + 3 log 5 -5 log 2

To find:-

Write 2 log 3 + 3 log 5 -5 log 2 as a single logarithm.

Solution:-

Given that

2 log 3 + 3 log 5 -5 log 2

We know that

log a^m = m log a

=>log 3^2 + log 5^3 - log 2^5

=> log (3×3)+log(5×5×5)-log(2×2×2×2×2)

=> log 9 + log 125 - log 32

We know that

log (a×b)=loga + log b

=> log (9×125) - log 32

=> log 1125 - log 32

We know that

log (a/b) = log a- log b

=> log (1125/32)

Answer:-

2 log 3 + 3 log 5 -5 log 2 = log (1125/32)

Used formulae:-

• log(ab)=log a+ log b

• log(a/b)=log a - log b

• log a^m = m log a