## anonymous one year ago Log Question:

1. anonymous

$\log _{10} 1/\sqrt{10}$

2. anonymous

Sqrt 10/ 10 is wrong :(

3. Nnesha

$\log_{10} \frac{1}{\sqrt{10}}$ like this ?

4. anonymous

Change of base: $$\log_a (x) =\dfrac{\log_b (x)}{\log_b (a)}$$

5. anonymous

Oh yes! Lol

6. Nnesha

you can convert square root to an exponent if you want or use change of base formula

7. anonymous

log(a/b)=log a-log b so the given expression becomes log 1-log sqrt 10 =-log sqrt 10 =-log (10)^1/2=-1/2

8. anonymous

Lets take $$x=\dfrac{1}{\sqrt{10}}$$

9. Nnesha

$\sqrt{y}$ 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

10. anonymous

So it would be $\log 1/\sqrt{10} /\log 10$ ??

11. anonymous

Oh oh okay

12. anonymous

\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}

13. anonymous

Wow thanks for all the support :o

14. Nnesha

typo (10)^{1/2} remember the exponent rule when move base from the numerator to denominator sign of the exponent would change $\huge\rm \frac{ 1 }{ x^{-m }}= x^m$

15. anonymous

Yes oh my gosh thank you @Nnesha

16. Nnesha

u 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