how do you do logarithms using a calculator? log3 81 = 4? how?

Question

hi
i was wondering how you do logarithms using a calc.
one of the examples in my book is log3 81 = 4. but i dont know how you get that answer using a calculator. how do u imput it into the calculator? ive tried brackets but they dont help. can any one help? thanks

Answer 1

I'll assume that you know what log means, and you just need to know which buttons to push. Most calculators have keys marked "ln" for natural log, and "log" for log base 10. Since you want a log base 3, you have to do a little more work than just hitting the log (or ln) button.

For the example you give, you should hit the following keys:
81
ln key
divide key
3
ln key
= key

After each step, you should see the following in your display:

81
4.394449
4.394449
3
1.098612
4

So the answer is 4, as expected.

This is based on the idea that
log-base-n (x) = ln (x) / ln (n)

Answer 2

I don't think you can directly take a log base 3 of a number. You may need to convert: loga b = ln b / ln a try diving ln 81 by ln 3. You should still get 4.

Answer 3

calculator has logarithms only with base 10. lg=log10.