Logarithmic Functions

Jules Bruno
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so, without using a calculator, determine the answer to the following questions. So here we have long of 1.0 times 10 to the five. So just like up above, the log is getting distributed to the one end to the 10 to the fifth. So we're gonna say here because they're multiplying. What this really means is we have long of one plus log off 10 to the fifth. Remember up above, we said that log of one is equal to zero, and then this is logged based 10. So this cancels out with this, giving us five at the end. So here, log of that number would be five. Now, this is easy to remember in terms of figuring out the log of an answer really quickly. But if this numbers happens to be a number different from one, then it's best toe and put it into your calculator. Because if it's log of any other number, this part won't be equal to 10 and you haven't memorized what those numbers are because you have your calculator. So again, this works best when we have long at 10 times 10 to any power, and then finally this one here we have a log of 10. We want to change this. So we're going to say that if we move this over and change to scientific notation, then we have log off 10 times 10 to the negative four. So it just becomes like the one we just did. The law gets distributed to both. So this is log of one plus log off. 10 to the negative. Four long of one is just zero. This is base 10 which cancels out with this, which gives me negative four. So it's zero plus negative four. So the answer he would be negative for is my final answer. So these are just the basics. When it comes to log functions, they're gonna become important when we're talking about chapters dealing with chemical kinetics also will come in handy when we're talking about determining Ph or P o. H off different solutions. That's when log functions really come out. And we have to do different types of mathematical manipulations to get our answer at the end. But for now, just remember the basics when it comes toe these blogged functions here