Question

How do I simplify this expression: 10^(log500)? Is it: log(500^10) on the calculator?

Answer 1

\(\log(x)\) and \(10^x\) are inverse functions, which means
\[\log(10^x)=x\] and \[10^{\log(x)}=x\]

Answer 2

or in english, \(\log(500)\) is the number you would raise ten to, to get 500
therefore it must be the case that \(10^{\log(500)}=500\)

Answer 3

wait how is log(x) an inverse of 10^x, sorry for the late reply D:

Answer 4

you can see this is the case as follows. lets say:\[\log_{10}a=b\implies a=10^b\]agreed?

Answer 5

and I agree.

Answer 6

ok, so we can then say:\[10^{\log_{10}a}=10^b\]agreed?

Answer 7

since we said:\[\log_{10}a=b\]

Answer 8

but we also showed that:\[10^b=a\]therefore:\[10^{\log_{10}a}=10^b=a\]

Answer 9

hope that makes sense?

Answer 10

yes oh..

Answer 11

thank you! :D

Answer 12

so in general we can say:\[b^{\log_bx}=x\]

Answer 13

yw :)