# How would you solve this logarithmic equation with both $\log n$ and $n$ terms?

I have a small logarithm related question that I do not seem to understand how to solve.

If a program takes $\log n$ microseconds to run a program of size $n$, what is the maximum size of a program that can run in $1$ second? Here, the base of the logarithm is $2$.

I end up with an equation - $(n 10^6)/ \log n =$ maximum size of the program that can run in $1$ second. However, I'm unsure on how to solve this further.

The answer I found for this question is $2^{(10^6)}$. However, the steps to obtain this answer were not shown. May I please know how to solve this question?

$$\log n=10^6$$
or the time it takes to run a program of size $n$ is one million microseconds. Now just solve for $n$.
• @user3705895 I think I more or less said it in English. "The time it takes to run a program of size $n$", which according to your problem is $\log n$, "is (equals) one million microseconds." – Mike Jan 7 '15 at 11:16