Question

if log(1234) = 3.0913 , log(769874)=5.88642) , find the value of \[\sqrt[8]{0.000000001234}\]

Answer 1

@satellite73 @FoolForMath

Answer 2

Hint:

\[\log_b(y) = x \equiv b^x = y\]

Answer 3

@Hero No idea!

Answer 4

is that first one log base ten?

Answer 5

yes all are with base 10

Answer 6

b = 10

Answer 7

then
\[\log(\sqrt[8]{.000000001234})=\frac{1}{8}\log(1234\times 10^{-12})\]

Answer 8

ok

Answer 9

check that i counted the decimal places correctly

Answer 10

u r correct

Answer 11

Is FFM still typing?

Answer 12

aka Across

Answer 13

you get
\[\frac{1}{8}\left(\log(1234)+\log(10^{-12})\right)\]
\[\frac{1}{8}\left(\log(1234)-12\right)\]

Answer 14

\[ x =\sqrt[8]{0.000000001234}= (1234 \times 10^{-12})^{\large \frac18} \] \[ \implies \log x = \frac 18 \times (\log 1234 -12 ) \]

Answer 15

hard for me to count that high, but if @FoolForMath got the same thing, then i guess it must be right

Answer 16

yup"

Answer 17

so wat is up next!

Answer 18

nothing
you are done
replace \(\log(1234)\) by 3.0913

Answer 19

i miss across

Answer 20

Plzz help

Answer 21

what do you need?

Answer 22

the answer should be 0.0769874

Answer 23

after solving urs i got -1.11358

Answer 24

I got 0.0769874 as well

Answer 25

then plz show it lol

Answer 26

i don't know.
\[\frac{1}{8}\left(\log(1234)-12\right)=\frac{1}{8}\left(3.0913-12\right)\] then a calculator

Answer 27

1/8 of a negative number?

Answer 28

@satellite73, we don't need a calculator,

\[\log x = \frac 18 (3.0913-12) = -1.11359 =-2 + 0.88642\] \[\implies x= 10^{-2} \times \text{ Antilog}( 0.88642)=0.0769874 \]

Answer 29

You only came up with that after the fact

Answer 30

?

Answer 31

you are telling me i want to compute
\[\log x = \frac 18 (3.0913-12) = -1.11359 =-2 + 0.88642\] with pencil and paper?

Answer 32

Yes, that's what we are supposed to do in exam :)

Answer 33

This is a typical entrance problem.

Answer 34

that is why i do not take exams. but lets say for a minute that you actually managed to do that
explain how i am going to compute
\[ x= 10^{-2} \times \text{ Antilog}( 0.88642)=0.0769874\]

Answer 35

lol

Answer 36

yeah, without a calculator @FFM

Answer 37

thzz

Answer 38

By reading the question once again.