Question

2ln10-ln5 as a single logarithm?

Answer 1

Any ideas on where to start?

Answer 2

nope

Answer 3

Are you familiar with any logarithm properties?

Answer 4

kind of

Answer 5

Are you familiar with the idea that y*ln(x) can be rewritten as ln(x^y) ?

Answer 6

okay, yeah sure

Answer 7

what about the idea that ln(x) - ln(y) = ln(x/y) ?

Answer 8

hmmm, yes

Answer 9

that's great

Answer 10

so 2ln(10) = ln(10^2) using the first property I wrote out

Answer 11

ln(10^2) = ln(100)

So

2ln(10) - ln(5)

becomes

ln(100) - ln(5)

with me so far?

Answer 12

yes sir

Answer 13

now use the second property to get

ln(100) - ln(5) = ln(100/5) = ln(20)


So ln(100) - ln(5) = ln(20)


which means 2ln(10) - ln(5) = ln(20)

Answer 14

oooooohhhhh, okay, makes sense thanks so much :)