Thread: Hi all ....

Hi
In this question How I know 0,000001 = 10^-2
Is there a way ? Is there a way by Calculator ?

Originally Posted by r-soy

Hi
In this question How I know 0,000001 = 10^-2
Is there a way ? Is there a way by Calculator ?

this is wrong,..

$\displaystyle 0,000001 = \frac{1}{100000} = 10^{-6} $ not $\displaystyle 10^{-2}$

sorry i mean 0,0001 = 10^-2

i can't undertand your way


Is there another way ?

Originally Posted by r-soy

sorry i mean 0,0001 = 10^-2

i can't undertand your way


Is there another way ?

0,0001 = 10^-2 is wrong too.

hhh i am confused

i mean 0,0001 = 100^-2

see the image and see the solving

Remember that $\displaystyle \log_a{b}=c \Longleftrightarrow\ a^{c} = b$, with $\displaystyle \log_a{b}=c$ well defined.

What it's written in yor exercise is just the aplication of the above.

Thus, you know $\displaystyle \log_b{0,0001}=-2 \Longleftrightarrow\ b^{-2}=0,0001$, but also know $\displaystyle 0,0001=10^{-4}=(10^{2})^{-2}$, because a propertie of powers says $\displaystyle (a^{b})^{c}=a^{bc}$ with $\displaystyle (a^{b})^{c}$ well defined.

Therefore, $\displaystyle b=100$

Without logarithms, 0,0001 ("one ten thousandth") means 1/10000= 1/(10)(10)(10)(10)= 1/10^4= 10^(-4).

0,01= 1/100= 1/(10^2)= 10^(-2).

Easy way- count the number of "decimal places"= 0,0001 has four places so is 10^(-4), 0,01 has 2 places so is 10^(-2).