Question

Simplify the expression, if possible (Rewarding medals)

log 10^5

log 10

log 10^-4

log 10^-1

log 1

log 3√100

log 1/100

log 1/10

log 10^4.7

log 10^2x+4

Answer 1

I'm not going to answer all these, but I'll show you a few of the log rules you'll be using in simplifying them. First off:
\[\log(x^a)=alog(x)\]In other words, when you have a base raised to a power inside a log, the exponent can drop down in front. So, in your first example:
log (10^5)=5log(10)

Answer 2

The other rules you'll want are the addition and subtraction of logs:
\[\log(ab) = \log(a) + \log(b)\]If we have two quantities multiplied together inside a log, we can split it into two logs, one for each quantity, added together.
\[\log(\frac{ a }{ b }=\log(a) - \log(b)\]If we have division, then we do the same thing, but we subtract the logs.

Answer 3

I have worked them out I basically want to check my answers...

log 10^5= 5
log 10=1
log 10^-4=0.0001
log 10^-1= 0.1
log 1= 0
log 3√100=3

Answer 4

The first two are correct, the next two are not. It looks like you simplified the 10^-4 and wrote it in decimal form, then just forgot about the log. You could use the first rule I showed you, since you have an exponent inside. So put the -4 to the front:
-4log10=-4(1)=-4