loga75+loga2

I assume we have this

log(a)(75) + log (a)(2)

By a property of "logs" ......    log(a)(b) = log(a) + Log (b)

So this gives us

log(a)(75) = log(a) + log(75)

And log(a)(2) = log(a) + log(2)

So, putting everything together, we have

log(a)(75) + log (a)(2) = log(a) + log(75) + log(a) + log(2)

= 2log(a) + log(75) + log(2)

But note, by "reversing" the log property above, I can write

2log(a) + [log(75) + log(2)]  as

2log(a) + [log(75)(2)] =

2log(a) + log(150)

Note, now that log(150) = log(10)(15) = log(10) + log(15)

And log(10) = 1

So we really have is..... 2log(a) + log(15) + 1

And another "log" property says that alog(b) = log(b)^a

So 2log(a) becomes log(a)²

And the final result is just

log(a)² + log(15) + 1

Re: loga75+loga2

Mmmmmm....after I looked at this again , I think you MIGHT have meant

log 75 + log 2

By a property of "logs" ......   log(a) + log (b)  = log(a)(b)

So, log 75 + log 2 = log(75)(2) = log(150) = log(10)(15) = log 10 + log 15

But, log 10 = 1

So, we have........ 1 + log 15

And that's it  (I hope........ )

Hey Chris, 

Why do you think it is base 10???

My interpretation

$$log_a 75+log_a 2
=log_a 150$$

And that is the end of the story