Question

how to interpret a real number in exponent

i got stuck when doing logarithms :

if u take log, for the numbers from 10 to 100, you would get the output [1, 2]

which means, \(\log 10 \) to \(\log 100\) will cover all the real numbers range [1, 2]

Answer 1

should i see the real exponent as, integer + fraction ? and then multiply the integer i get, with a radical ? could somebody plz explain....

Answer 2

yes, that's right

Answer 3

is that the only way

Answer 4

rational exponent i can split as integer * radical.

but what about irrational exponent.. idk if im even ready to think of it. i dont understand the rational exponent itself fully yet.. .

Answer 5

\(10^{1.6789}\) = ?

Answer 6

im sure it lies between [1, 2]

Answer 7

oh sorry the log value of it i mean.. . but how to think of it with out logs.. hmm

Answer 8

i mean outside logs, where we use this

Answer 9

LOG simply strips the base 10 and returns the exponent. so in your case, \[\log_{}10^{1.6789}=1.6789 \]

Answer 10

yes,

Answer 11

how to find the value of \(10^{1.6789}\)

Answer 12

before the invention of calculators, log is a convenient way of multiplying and or dividing large or small numbers

Answer 13

ya like, \(10^1 = 10, \) and \(10^2 = 10 \times 10 = 100\)

\(10^3 = 10 \times 10 \times 10 = 1000\)

Answer 14

how can we think of/ or find the value of \(10^{1.6789}\)

Answer 15

that is an interesting question if you have to compute it manually

Answer 16

oh i dont think i wanto compute it manually, i just wanto know how it can be understood, thats all

Answer 17

\(10^{1.6789} = 10^{1+.6789} = 10^1 + 10^{.6789}\)

Answer 18

the equivalent question to that is "what is that number whose logarithm is 1.6789?"

Answer 19

\(10 + 10^{.6789}\)

Answer 20

thats right, logarithms are same as exponents

Answer 21

the equation is wrong. it should be \[10^{1.6789}=10^{1}10^{0.6789}\]

Answer 22

so i would like to understand these, either completely in logarithms, or completely in exponetns., without mixing both as we wud go in circles..

Answer 23

ah thank u yes.s.

Answer 24

\(10^{1.6789}=10^{1}10^{0.6789} = 10 . 10^{\frac{1}{somthing}}\)

Answer 25

can i write something like that, and take root of 10

Answer 26

idk if there is some other elegant way to put these..

Answer 27

\(10^{1.6789} = 10 . \sqrt[somthing]{10}\)

Answer 28

and compute the root ? thats how computer does the calculation ?

Answer 29

\(\huge 10^{1.6789} = 10 . \sqrt[somthing]{10} = 10 . \sqrt[1.5]{10} \)

Answer 30

i knw i can figure out extracting roots manually.. . it makes bit sense.. but is there any other interpretation for this, easy one ?

Answer 31

@hartnn @sauravshakya

Answer 32

idk, what exactly u wanna do by interpreting, but u can 'guess' that value of 10^1.6789 is around 50, (because its definitely between 10 and 100, and its not near of either of them)