# Thread: Trying to understand exponents and logs

1. ## Trying to understand exponents and logs

Let me try this again, without word formatting.

Somewhat new to algebra 54-year-old took up math as a hobby<br>I am not sure if this is a log question or exponent question but in the equation
log 3.0112 = 1050
mathematically how do you get 1050 from 3.0211. I mean I understand log10 = 1, log100 = 2, log3 = 1000, etc. But the decimal points in-between are a mystery. I get stuck after 10*10*10= 3.0, where does the .0211 come in to get 1050<br>

2. ## Re: Trying to understand exponents and logs

In future, do not make a new post covering the same problem ... attach your correction to your initial post. Thank you.

log 3.0112 = 1050
$\log_b(y) = x \implies b^x = y$

... maybe you meant to type $\log(1050) = 3.0212$ ?

3. ## Re: Trying to understand exponents and logs

Originally Posted by johnymac67
Let me try this again, without word formatting.

Somewhat new to algebra 54-year-old took up math as a hobby<br>I am not sure if this is a log question or exponent question but in the equation
log 3.0112 = 1050
mathematically how do you get 1050 from 3.0211. I mean I understand log10 = 1, log100 = 2, log3 = 1000, etc. But the decimal points in-between are a mystery. I get stuck after 10*10*10= 3.0, where does the .0211 come in to get 1050<br>
Are we to assume that this logarithm is to base 10? "log(3.0112)= 1050" is false. No is it true that log(1050)= 3.0112! What is true is that log(1050)= 3.0211. That is true because $10^{3.0211}= 1050$ (to the nearest integer). You know that $10^3= 1000$. You also, I presume, know that $10^{3.0211 10^{3+ 0.0211}= (10^3)(10^{0.0211})$. The rest is true because $10^{0.0211}= 1.050$.

How do we determine that? There are a number of (very tedious) numerical ways of calculating that.

Fortunately other people have already done that and put the values into tables that were put into books. And today, we have calculators that find logarithms and exponentials. Enter 1050 into the calculator that comes with Windows, click on the 'log' "key" and you get 3.0211892990699380727935052671233 which rounds to 3.0211 (not 3.0112).