anonymous
  • anonymous
PLEASE HELP WITH LOGs IF loga5=2.32 and loga3=1.59, find loga45
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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MrNood
  • MrNood
so - note that 45 = 9*5 you have loga 5 and oyu have log a 3 what is the relationship betweem 3 and 9?
anonymous
  • anonymous
im not sure
MrNood
  • MrNood
2^2 = 4 3^2 = ?

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anonymous
  • anonymous
9
MrNood
  • MrNood
SO 9 = 3^2 So if loga3 = 1.59 what is loga 3^2
anonymous
  • anonymous
would it be 3
MrNood
  • MrNood
no this is the key point of th equestion you must be studying logs and their properties so see if you can find a way of simplifying \[\log _{a} x ^{n}\]
anonymous
  • anonymous
well that would be n times loga(x)
MrNood
  • MrNood
good - you have solved the question! so what is \[\log _{a }3^{^{2}}\]
anonymous
  • anonymous
2 times loga(3)
anonymous
  • anonymous
loga(5*3)
MrNood
  • MrNood
no - you want to find loga(5 * 3^2)
anonymous
  • anonymous
i mean 5*9
anonymous
  • anonymous
so loga(5)+loga(9)
MrNood
  • MrNood
you got it and you have both those numbers..... add em up!
anonymous
  • anonymous
but the answer key says 5.50 is that wrong?
MrNood
  • MrNood
no you wrote just now what log 3^2 is (it is in YOUR post above... what is log 9? what is log 5 add tehm together
anonymous
  • anonymous
i got 2?
MrNood
  • MrNood
YOU wrote above "well that would be n times loga(x) so what is log 9 ( it is the same as log 3^2)
anonymous
  • anonymous
oh so 2 loga (3)
MrNood
  • MrNood
yes - you already wrote that so now oyu can work out loga(5)+loga(9)
anonymous
  • anonymous
but im typing that into my calculator and getting 2?
MrNood
  • MrNood
you don't need a calculator you are given the numbers in the question what is loga 3? what is 2 loga 3? what is loga 5? soooo - what I slog a 45 you have DONE all the work - you just need to put the steps together you are using the calculator wrong - but that doesn't matter now - you don't need the calculator
MrNood
  • MrNood
anyhow - you can't use calc because you don't know what a is
anonymous
  • anonymous
oh ok i forgot about the numbers so i got 5.5 with the number
anonymous
  • anonymous
thank you so much!
MrNood
  • MrNood
np
anonymous
  • anonymous
if it's not too much to ask, could you also help me with this last one? i have to condense \[\log_{4} 128-1\]
MrNood
  • MrNood
OK it would be good if this was log 4 x - log 4 y Can you make it look like that?
anonymous
  • anonymous
i dont think we learned that
MrNood
  • MrNood
so if it was to look like I said tehn we can see that log4 y = 1 what is y? (think about the meaning of what loga really means) (I think you seem to have the skills to do this...)
anonymous
  • anonymous
do you mean y=128 or do you want it in exponential form?
MrNood
  • MrNood
no - it is not y=128 what is \[\log_{10} 10\] or \[\log_{e} e\]
anonymous
  • anonymous
1?
MrNood
  • MrNood
yes so logn n =1 for any n so we can write your original equation as log4 128 - log 4 4 can oyu simplify from there?
anonymous
  • anonymous
i got 32 but the answer is 5/2
anonymous
  • anonymous
because i did log4 128/4
MrNood
  • MrNood
ok - you have not quite done the simplification properly what is log a - log b?
anonymous
  • anonymous
would you use the change of base property
MrNood
  • MrNood
no - sorry - I was being slack in notation - forget that you are nearly there go back to log4 128 - log 4 4 can oyu simplify from there? And try again - you made a small mistake....
anonymous
  • anonymous
log4 (128/4)?
MrNood
  • MrNood
yes
anonymous
  • anonymous
oh i got i! you convert it to exponential so you get 5/2
anonymous
  • anonymous
thanks so much!
MrNood
  • MrNood
not sure I follow that
MrNood
  • MrNood
log4 (128/4) = log4 (32) which IS 5/2 but I need to see how you got there....
anonymous
  • anonymous
i got 4^x =32 and then you do (2^2)^x=(2^5) and 2x=5 is 5/2
MrNood
  • MrNood
OK - I see 32 = 2^5 so 4^5 /4^2
anonymous
  • anonymous
yeah
MrNood
  • MrNood
well done
anonymous
  • anonymous
thanks so much!!

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