### Home > CCA2 > Chapter 5 > Lesson 5.2.4 > Problem5-96

5-96.

Last night, while on patrol, Agent 008 came upon a spaceship! He hid behind a tree and watched a group of little space creatures carry all sorts of equipment out of the ship. But suddenly, he sneezed. The creatures jumped back into their ship and sped off into the night. 008 noticed that they had dropped something, so he went to pick it up. It was a calculator! What a great find. He noticed that it had a $\boxed{\text{LOG}}$ button, but he noticed something interesting: $\log10$ did not equal $1$! With this calculator, $\log10\approx0.926628408$. He tried some more: $\log100\approx1.853256816$ and $\log1000\approx2.779885224$.

1. What base do the space creatures work in? Explain how you can tell.

You are looking for the base of the log; let’s call it $b$. So $\log_b(10)\approx0.926628408$.
Rewrite that equation in exponential form. How can you solve it?
Use Guess and Check if you can’t think of another method.
Does the same base work for $\log100$ and $\log1000$?

2. How many fingers do you think the space creatures have?

How many fingers do you have? What is the base of the log on your calculator?