Question

Write the given expression as a single logarithm:
4log(5x) - 5[log(x) - log(y-5)]

Answer 1

Can you write this one in single logarithm?
log(x) - log(y-5)

Answer 2

I don't know how to

Answer 3

log a - logb = log (a/b)
Can you do it now?

Answer 4

So would it be log(x/y-5)?

Answer 5

Yep, to be exact:
log ( x / ( y -5) )

Answer 6

so 5[log(x) - log(y-5)] = log ( x / ( y -5) )^5

Answer 7

Now, do you know what to do with 4log(5x) ?

Answer 8

No I was trying to figure it out but cant

Answer 9

Did you see what I've done with number 5, then
try to do similarly with number 4 : 4log(5x)

Answer 10

4log(5x) -5(log(x) - log(y-5)) = log(5x)^4 -5(log(x/(y-5))) =
= log(5x)^4 - log(x/(y-5))^5 =log((625x^4)/((x/(y-5))^5) =
= log(625x^4)/((x^5)/(y-5)^5) = log(((625x^4)(y-5)^5)/(x^5)) =
= log((625(y-5)^5)/x)