need help with logarithm please

[btown]

The question is-
express as a single logarithm:
log₃40 - log₃ 15 + 2 log₃ (3/5)

The answer I got was:
log₃ (16/5)

However my textbook says the answer is:
b= π/2

I've literally no idea how this could be the answer. I'm thinking it might even just be a printing error?

Can anyone help explain?

 

[Ishuda]

The question is-
express as a single logarithm:
log₃40 - log₃ 15 + 2 log₃ (3/5)

The answer I got was:
log₃ (16/5)

However my textbook says the answer is:
b= π/2

I've literally no idea how this could be the answer. I'm thinking it might even just be a printing error?

Can anyone help explain?

I agree - I think it is a print error if the answer is given as b= π/2. In any case, there is no b is the problem you give, so something is strange.

For the problem itself, I assume you used the properties of logs. That is, assuming all logs are to the same base as they are here,
a log(b) = log(b^a)
log(a) + log(b) = log(a * b)
and
log(a) - log(b) = log(a / b).
In that case we have
log₃40 - log₃ 15 + 2 log₃ (3/5)= log₃(40 / 15) + log₃[(3/5)²] = log₃[(8/3) (3/5) (3/5)]= log₃(24/25)
unless I made a misteak somewhere in the arithmetic.

 

[btown]

Thank you!!!

Yes I think that's the right answer. I'd made a couple of mistakes in my workings but I've got the same answer now