Solve the Reciprocal Expression: 1/ln8 Step-by-Step

Reciprocals and negatives are completely different! $\frac{1}{\ln 8}$ is positive (about 0.48), while $-\ln 8$ is negative (about -2.08). Never confuse reciprocals with opposites.

Think of it as "new base goes on bottom": $\log_a b = \frac{\ln b}{\ln a}$. The base you want (a) goes in the denominator, and what you're taking the log of (b) goes in the numerator.

By definition, $\ln e = \log_e e = 1$ because any number raised to the power 1 equals itself. This is like asking "e to what power gives e?" The answer is 1.

Yes! Calculate $\frac{1}{\ln 8}$ and $\log_8 e$ separately. Both should give approximately 0.4807. If they match, your algebraic work is correct!

The same method works! For $\frac{1}{\ln a}$, the answer is always $\log_a e$. Just replace 8 with whatever number you have.