When I press "log" and 2 into my calculator I get 0.301029995.... Why?

Question

What is this log my calculator speaks of? Thank you.

Answer 1

This is called the "log base 10", or more fully the logarithm to base 10. What it means is that 10 raised to this power is 2.

For instance, you will find that
log 100 = 2
log 1000 = 3
log 1000000 = 6
log 0.1 = -1

In general, if 10^x = y then log y = x.

Your calculator will also have a "ln" button. This does the same thing, but with the base e rather than 10. (Euler's number e is a special number with value approximately 2.71828.)

You can also calculate logarithms to any other base, by the rule of logs:
log (base a) of x = log (base b) of x / log (base b) of a
for any b > 0.

So, for instance, 2^3 = 8, so log (base 2) of 8 = 3. You can verify this on your calculator by evaluating log 8 / log 2.

Answer 2

A log is used in higher math. It is the power of 10 needed to obtain the number. 10^.301029995 = 2.

Adding logs has the same effect as multiplying the base numbers. Back before calculators, slide rules used this principal to multiply numbers.

Answer 3

the base 10 log of 2 is 0.301029...
This means that 10 raised to the .301029 power = 2.

Logs are useful in solving many equations, especially problems involving exponents. For example : 4 to what power = 43
[4^x = 43] the answer is the number equal to log 43/log4, or 2.713. 4^2.713 = 43

Answer 4

that means the 10^0.301029995=2