Question

Log Question:

Answer 1

\[\log _{10} 1/\sqrt{10}\]

Answer 2

Sqrt 10/ 10 is wrong :(

Answer 3

\[\log_{10} \frac{1}{\sqrt{10}}\] like this ?

Answer 4

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

Answer 5

Oh yes! Lol

Answer 6

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

Answer 7

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

Answer 8

Lets take \(x=\dfrac{1}{\sqrt{10}}\)

Answer 9

\[\sqrt{y} \] 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

Answer 10

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

Answer 11

Oh oh okay

Answer 12

\[\begin{align} \log_{10} \left(\frac{1}{\sqrt{10}}\right) &=\frac{\log\left(\frac{1}{\sqrt{10}}\right)}{\log(10)}\\& = \frac{\log(1)-\log(\sqrt{10})}{\log(10)} \\&=\frac{-\frac{1}{2}\log(10)}{\log(10)}\\&=-\frac{1}{2} \end{align}\]

Answer 13

Wow thanks for all the support :o

Answer 14

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

Answer 15

Yes oh my gosh thank you @Nnesha

Answer 16

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