Question

Please Need Urgent Solution For This Problem. Mention How to Solve .Give Proper Steps. Answer All The 3 Questions Accordingly.

Answer 1

log base 10 x = a
i) 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)

Answer 2

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