# What does increasing the input size by a factor of 100 do to a linearthimic algorithm with the complexity of 2nlog(n)

So far what I've tried to do is break this into parts and work from there

So for the $$2n$$, increasing by a factor of 100 means the runtime goes up by 100 times

But I get stuck with the log(n) part. Initially, I had thought this gets reduced down to $$2n$$ as $$log(100) = 2$$ but that didn't seem to work.

• What does it look like plugging a few more values? Is the base of the logarithm specified? Is there a recognizable relation between $7n, 7^2n, 7^3n$? \$n, n^2, n^3? – greybeard Aug 6 '20 at 3:52