Question

write 4log4+2log5-log 15 as single logarithm

Answer 1

Thanks for the question!

It is definitely a very interesting question to solve and do some brainstorming.

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4 log 4 + 2 log 5 - log 15

=  log 4^4 + log 5^2 - log 15

= log 256 + log 25 - log 15

= log (256 x 25) - log 15

= log 6400 - log 15

= log 6400/15

= log 1280/3

We know, log a + log b = log ab and log a - log b = log a/b

Answer 2

Answer:

Answer=log(1280/3)

Step-by-step explanation:

Given that:

⇒4*log(4)+2*log(5)-log(15)..............(i)

Solution:

according to log property

⇒2*log(5)=log(5)²

and equation (i) will becomes

⇒4*log(4)+log(5)²-log(15)

according to property of log

⇒log(a)-log(b)=log(a/b)

so,

so equation (i) will becomes

⇒4log(4)+log(25/15)

⇒4log(4)+log(5/3)

according to log property

⇒log(a+b)=log(a*b)

so,

⇒log(4^4*5/3)

⇒log(1280/3)   Answer