Hey Nadine, so logarithms seem pretty complicated but if you look at them as exponents.. then they're actually pretty simple if you get the basic gist of them. So to answer your first question as to why 10^-2 is 1/100, this is just a math rule that you kind of have to remember. With exponents any time you have a number raised to a negative number that automatically make that number a fraction. It makes it 1 over whatever that number would be if it were positive. So in the picture I wrote a few examples... 10^1=10 right? So then 10^-1 would be 1/10, 10^2=100, so then 10^-2=1/100. Its just one of those pesky rules of exponents and fractions you have to remember. As far as how to use this with log base 10, well like I said think of a logarithm as an exponent but instead you are kind of working out of order. The answer for the exponent form and the log form will be different as you can see above.. Does that make sense? I guess the big takeaway here is that you have to think of these guys as out of order exponents! If you need any further clarification please let me know !

Another thing to note is that your calculator may not calculate the log of any number OTHER than 10, most calculators use log base 10 as their default setting. So if you wanted to calculate one of the ones I have above then you would have to create a function that would look like: log(16) / log(2) and you should get 4 as your answer ! Hope this helps !

Hey Nadine, so logarithms seem pretty complicated but if you look at them as exponents.. then they're actually pretty simple if you get the basic gist of them. So to answer your first question as to why 10^-2 is 1/100, this is just a math rule that you kind of have to remember. With exponents any time you have a number raised to a negative number that automatically make that number a fraction. It makes it 1 over whatever that number would be if it were positive. So in the picture I wrote a few examples... 10^1=10 right? So then 10^-1 would be 1/10, 10^2=100, so then 10^-2=1/100. Its just one of those pesky rules of exponents and fractions you have to remember. As far as how to use this with log base 10, well like I said think of a logarithm as an exponent but instead you are kind of working out of order. The answer for the exponent form and the log form will be different as you can see above.. Does that make sense? I guess the big takeaway here is that you have to think of these guys as out of order exponents! If you need any further clarification please let me know !

Another thing to note is that your calculator may not calculate the log of any number OTHER than 10, most calculators use log base 10 as their default setting. So if you wanted to calculate one of the ones I have above then you would have to create a function that would look like: log(16) / log(2) and you should get 4 as your answer ! Hope this helps !