So continue where we left off. It says without using a calculator, determine the answer to the following questions. So remember we have a log of 1.0×10-7 here. Because they're multiplying, we can distribute the log to the one and to the 10-7. Because they're multiplying, it really means that they're being added together.
From up above we saw that log of one is equal to 0 and then we saw up above that this is log base 10 so that 10 in this 10 can be thought of canceling each other out. So then what would be left behind would be this -7. So we have 0 + -7. So our answer at the end will be -7 for this one.
Log of 1000. Think about it, how else could I write 1000? I could write it as 103, so this cancels out. Cancels out. So we'd be left with a value of 3. Double check. Plug it into your calculator. See if you get the same exact answer.
Remember, if you have a number to a power the times 10 to a power, you should put it in parentheses in your calculator. Otherwise you may get the incorrect answer. So you do log ( 1.0×10-7 ) and get your answer of -7.
So we've done these two. Attempt to do this next example on your own. See if you get the answer. You can double check by punching it into your calculator or by coming back and taking a look at my video explanation on how to approach this question as well.