1. The problem is to solve an equation or expression without using logarithms. 2. Since the user did not specify the exact problem, let's consider a common example: solving for $x$ in an exponential equation like $2^x = 8$ without logarithms. 3. We use the fact that $8$ can be written as a power of $2$: $8 = 2^3$. 4. So the equation becomes $2^x = 2^3$. 5. Since the bases are the same and the function $2^x$ is one-to-one, the exponents must be equal: $x = 3$. 6. Therefore, the solution is $x = 3$. 7. This method avoids logarithms by expressing both sides with the same base and equating exponents.