anonymous
  • anonymous
what is the answer of log base 5 of root 10..?? plz rply
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\log _{5} \sqrt{10} ?\]
ash2326
  • ash2326
@sana_kausar Can you simplify this?
anonymous
  • anonymous
@mrbarry... yes what's d answer fr it..??

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More answers

ganeshie8
  • ganeshie8
it has to be less than 1 cuz \(\sqrt{10}\) is less than 5
UnkleRhaukus
  • UnkleRhaukus
\[\log_5 \sqrt{10}=\log_5 10^{1/2}=\tfrac12\log_5 10=\tfrac12\log_5 (5\times2)=\]
anonymous
  • anonymous
\[\sqrt{10} is 0.5\]
primeralph
  • primeralph
|dw:1370156886289:dw|
ganeshie8
  • ganeshie8
1 Attachment
UnkleRhaukus
  • UnkleRhaukus
\[\large\boxed{\log_b b=1}\]\[\large\boxed{\log_b x=\frac{\log_c x}{ \log_c b}}\]
ganeshie8
  • ganeshie8
yeah 0.5 is right for \(\log \sqrt{10}\) @sana_kausar
ganeshie8
  • ganeshie8
but log by default is is base 10. the question here asking you to compute it for base 5
ganeshie8
  • ganeshie8
you can use change of base formula. look above at Unkle's reply.. \(\large \log_5 \sqrt{10} \) \(\large \frac{\log \sqrt{10} }{\log 5} \)
anonymous
  • anonymous
so the answer is coming to 0.71541..
ganeshie8
  • ganeshie8
Yes !
anonymous
  • anonymous
okz.. thanks...!!
ganeshie8
  • ganeshie8
np :)
dan815
  • dan815
|dw:1370157951519:dw|
dan815
  • dan815
i dunno what else from here!
dan815
  • dan815
|dw:1370158290039:dw|
dan815
  • dan815
so thats how that formula comes about xD
dan815
  • dan815
|dw:1370158410490:dw|
UnkleRhaukus
  • UnkleRhaukus
\[\log_xB^y=\log_x\overbrace{BBB\dots B}^{y-\text {times}}\\=\overbrace{\log_xB+\log_xB+\log_xB+\dots+\log_xB}^{y-\text {times}}\\=y\log_xB\]
dan815
  • dan815
how do u prove logx(BBBB)..--> logxB+logxB...
dan815
  • dan815
its like this
UnkleRhaukus
  • UnkleRhaukus
\[\large\boxed{\log_bxy=\log_b x+\log_by}\]
anonymous
  • anonymous
we can apply change of base formula...
dan815
  • dan815
|dw:1370159047462:dw|
dan815
  • dan815
|dw:1370159174656:dw|

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