SOLUTION: In general, how do I find the logarithm of the answer ex: evaluate 1776^53 I can get 53 Log 1776 = log x, but what is next?

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 Click here to see ALL problems on logarithm Question 167703This question is from textbook Algebra and Trigonometry : In general, how do I find the logarithm of the answer ex: evaluate 1776^53 I can get 53 Log 1776 = log x, but what is next? This question is from textbook Algebra and Trigonometry Found 2 solutions by stanbon, Edwin McCravy:Answer by stanbon(57307)   (Show Source): You can put this solution on YOUR website!1776^53 ------------ Let x = 1776^53 log(x)= 53*log(1776) log x = 53*3.24944... --------------- 10^(logx) = 10^(53*3.24944...) x = 10^172.2203... ================== Cheers, Stan H. Answer by Edwin McCravy(8908)   (Show Source): You can put this solution on YOUR website!Edwin's solution follows: In general, how do I find the logarithm of the answer ex: evaluate I can get , but what is next? ``` You could get your calculator and find which is and then mutiply that by to get . However that won't get you any closer to finding ! That's because calculators as a rule can only work directly with numbers less than , "1 google". You can't get on a calculator directly because that number is bigger than googol. Most calculators made today can do anything but give an overflow error message for a google and anything larger. However you can get larger numbers indirectly on your calculator. On my calculator I find that I can get directly as However when I try to get I get an overflow error message. We can break down this way: both of which can be found on the calculator: Then we can multiply those decimal parts, then add the exponents of ten and get So therefore However, that's not in scientific notation because is not less than 10, so we write it in scientific notation as , then substituting we have or adding the exponents of ten: Notice that we could have broken down in a number of other ways, for example: so . And so we have, as above: There is a slight difference between the two. I would guess that that latter is closer to the true value, but we could safely round either answer to this: Edwin```