Question

Indices and Surds question, thank you!

Answer 1

Given that 123^a=1000 and 0.123^b=1000, show that (1/a)-(1/b)=1

Answer 2

take log if know log otherwise something other

Answer 3

what is log

Answer 4

logarithmic

Answer 5

@Er.Mohd.AMIR Please, show me how.

Answer 6

without log, 0.123* 1000=123 , hence \(123^a =0.123^a*1000^a=0.123^b\)
then ?

Answer 7

yeah, how do you solve it without log?

Answer 8

Even with log, I got stuck also. :) how stupid I am . hehehe
alog 123 =b log 0.123
This is what I can derive : \(\dfrac{a}{b}=log_{123} 0.123\) and nothing else pops up.
\(123^{\color{red}{???}}=0.123\) ?

Answer 9

a log 123 =log 1000
1/a = log 123/log 1000
b log 0.123=log 1000
b log (123/1000)=log 1000
b (log 123-log 1000)=log 1000
1/b=(log 123-log 1000)/log1000
1/b=log 123/log 1000-1
1/b=1/a-1
1/a-1/b=1 hence proved.

Answer 10

how about without log?

Answer 11

i try out if i solve post it.

Answer 12

thank you!

Answer 13

123^a=1000
123=1000^1/a
and
0.123^b=1000
0.123=1000^1/b
123/1000=1000^1/b
123=1000^(1/b+1)
now 1000^1/a=1000^(1/b+1)
compiar powers
1/a=1/b+1
1/a-1/b=1
Hence Proved

Answer 14

Now Without LOG

Answer 15

Now i complete What i said.

Answer 16

Thank you so much @Er.Mohd.AMIR