Given , log( x base 10) =a log ( y base 10)=b we know according to rule of logarithm log ( x base y) =N then, x=y^N use this here
1) 10^(a-1)
let z=10^(a-1) take log both side log ( z base 10) =log (10^(a-1) base 10) =log ( 10^a.10^-1 base 10) =(a-1) now put a=log ( x base 10) log (z base 10)=(log( x base 10)-1) z=10^{log(x base 10 ) -1 }=x/10
in the same way 2) 10^2b= 10^2log (y base 10)=y^2
3) log (p base 10) =2a -b =2log (x base 10)-log (y base 10) =log(x^2/y base 10)
Answers & Comments
Verified answer
Log base 10 x = ai) x= 10^a
x/10 =10^a/10
⇒x/10 = (10)^a-1
2) log base10 y = b
⇒10^b = y
⇒(10^b)² = y²
⇒(10)^2b = y²
iii) log base 10 p = 2a -b
= 2log base 10 x - log base10 y
= log base 10 x² - log base 10 y
= log base10 (x²/y)
Verified answer
Given ,log( x base 10) =a
log ( y base 10)=b
we know according to rule of logarithm
log ( x base y) =N
then,
x=y^N
use this here
1) 10^(a-1)
let z=10^(a-1)
take log both side
log ( z base 10) =log (10^(a-1) base 10)
=log ( 10^a.10^-1 base 10)
=(a-1)
now put a=log ( x base 10)
log (z base 10)=(log( x base 10)-1)
z=10^{log(x base 10 ) -1 }=x/10
in the same way
2) 10^2b= 10^2log (y base 10)=y^2
3) log (p base 10) =2a -b
=2log (x base 10)-log (y base 10) =log(x^2/y base 10)
so,
p=x^2/y