A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Log Question:
anonymous
 one year ago
Log Question:

This Question is Closed

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

anonymous
 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 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Change 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0log(a/b)=log alog b so the given expression becomes log 1log sqrt 10 =log sqrt 10 =log (10)^1/2=1/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lets 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

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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\begin{align} \log_{10} \left(\frac{1}{\sqrt{10}}\right) &=\frac{\log\left(\frac{1}{\sqrt{10}}\right)}{\log(10)}\\& = \frac{\log(1)\log(\sqrt{10})}{\log(10)} \\&=\frac{\frac{1}{2}\log(10)}{\log(10)}\\&=\frac{1}{2} \end{align}\]

anonymous
 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 \[\huge\rm \frac{ 1 }{ x^{m }}= x^m\]

anonymous
 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
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.