# Logarithmic expression

How come

$$2^{n+1} > 10^{10}$$

gets simplified to

$$n > \frac{10}{\log 2 - 1}$$

I don't understand how the book got $-1$ there. Could somebody please explain? Thanks!

• NVMD! GOT IT! SORRY! – user275675 Sep 30 '15 at 22:55
• I presume that you suddenly recognized that taking the logarithm (base 10) of both sides give (n+1) log(2)= 10 so that n+ 1= 10/log(20 and it is that "+1" that becomes the "-1" on the right. – user247327 Sep 30 '15 at 22:58
• Do you mean $n\gt\frac{10}{log_{10}(2)}-1$ – Mufasa Sep 30 '15 at 22:59