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Melissa_Something
 one year ago
Log Question:
Melissa_Something
 one year ago
Log Question:

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Melissa_Something
 one year ago
Best ResponseYou've already chosen the best response.0\[\log _{10} 1/\sqrt{10}\]

Melissa_Something
 one year ago
Best ResponseYou've already chosen the best response.0Sqrt 10/ 10 is wrong :(

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1\[\log_{10} \frac{1}{\sqrt{10}}\] like this ?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Change of base: \(\log_a (x) =\dfrac{\log_b (x)}{\log_b (a)}\)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1you can convert square root to an exponent if you want or use change of base formula

jango_IN_DTOWN
 one year ago
Best ResponseYou've already chosen the best response.2log(a/b)=log alog b so the given expression becomes log 1log sqrt 10 =log sqrt 10 =log (10)^1/2=1/2

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Lets take \(x=\dfrac{1}{\sqrt{10}}\)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1\[\sqrt{y} \] can be written as \[\rm y^\frac{ 1 }{ 2 }\] so \[\rm \log_{10} \frac{ 1 }{ (10)^\frac{ 1 }{ 2 } }\] move the (10)^/2 at the numerator

Melissa_Something
 one year ago
Best ResponseYou've already chosen the best response.0So it would be \[\log 1/\sqrt{10} /\log 10\] ??

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1\[\begin{align} \log_{10} \left(\frac{1}{\sqrt{10}}\right) &=\frac{\log\left(\frac{1}{\sqrt{10}}\right)}{\log(10)}\\& = \frac{\log(1)\log(\sqrt{10})}{\log(10)} \\&=\frac{\frac{1}{2}\log(10)}{\log(10)}\\&=\frac{1}{2} \end{align}\]

Melissa_Something
 one year ago
Best ResponseYou've already chosen the best response.0Wow thanks for all the support :o

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1typo (10)^{1/2} remember the exponent rule when move base from the numerator to denominator sign of the exponent would change \[\huge\rm \frac{ 1 }{ x^{m }}= x^m\]

Melissa_Something
 one year ago
Best ResponseYou've already chosen the best response.0Yes oh my gosh thank you @Nnesha

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1u already got the answer so i'm just gonna work itout \[\log_{10} 10^{\frac{1}{2}}\] apply the power rule power rule \[\large\rm log_b x^y = y \log_b x\] \[\frac{1}{2} \log_{10}10\] log_{10} 10 = 1 so left wth 1/2
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