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Man hiding behind a tree. 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 LOG key icon button, but he noticed something interesting: log 10 did not equal 1! With this calculator, log10 ≈ 0.926628408. He tried some more: log 100 ≈ 1.853256816 and log 1000 ≈ 2.779885224. Homework Help ✎

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

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

You are looking for the base of the log; let’s call it b. So logb(10) ≈ 0.926628408.
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 log 100 and log 1000?

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