Question

what is log base 3 of 4

Answer 1

You need to find a value?

Answer 2

I need to compute it

Answer 3

Ok. Do you have a calculator with logs?

Answer 4

no I dont

Answer 5

you can use the calculator on the computer just turn it scientific view i should be there

Answer 6

You can use an online calculator.
A calculator will let you calculate logs base e or base 10, but not base 3.
That means you need the change of base formula.

Answer 7

sorry it should be there my key board is malfuntioning

Answer 8

\(\large \log_a x = \dfrac{\log_b x}{\log_b a} \)

Answer 9

You want \(\large \log_3 4\)

Using the formula above, you can turn it into a calculation involving log base 10, which a calculator can do.

\(\large \log_3 4 = \dfrac{\log_{10} 4}{\log_{10} 3} \)

Answer 10

so do I do this by hand? or would I punch this formula into a calc

Answer 11

You need a calculator.

Answer 12

ok, and when I put it in the calculator, i don't need to worry about putting in the 10 right, since that is like the default base?

Answer 13

Correct.

Answer 14

your calc (handheld calc) should understand the base is already 10 when nothing is there
however some online calc will think the base is something else however it doesn't matter in this case you could do
\[\frac{\log_{anything}(4)}{\log_{anything}(3)}\]
those anythings have to be same as each other of course
and the anything has to be a positive number not equal to 1

Answer 15

ok, I got 1.262 (rounded third decimal place) is this correct

Answer 16

Correct. That's what I got.

Answer 17

Now if you want to check, raise 3 to that power. You should get 4.
That's what logs are all about.

Answer 18

BTW, your calculator probably also has log base e, which is called the natural log, or ln, and that would have worked too.
The change of base formula allows you to change to any base you want.
Changing to base 10 or base e makes sense bec calculators usually can calculate those two bases easily with just a press of a button.