Question

Plzzz solv it fast 9 i ii iii

Answer 1

log( x base 10 ) = 2a
x = 10^2a
log ( y base 10) = b/2
y = 10^b/ 2
1) here figure not clear !!
by the way ,
if question ask write 10^a in term of x
then ,

from above ,
x = 10^2a
take root both sides
x½ = 10^2a×1/2

so, 10^ a = x½ = √x

ii) 10^(2b +1 ) in term of y

from above ,
y = 10^b/2

take both sides 4 power

y⁴ = ( 10^b/2}⁴ = 10^b×4/2 = 10^2b

multiply both sides into 10

10y⁴ = 10^(2b+1)
so, 10^(2b +1) = 10y⁴

iii) log( P base 10) = 3a - 2b

2a = logx
a = 1/2 logx
3a = 3/2logx
similarly ,

b/2 = logy
2b =4 logy

put this in above equation,

logP = 3/2logx -4logy
= log(x√x ) -logy⁴
=log( x√x/y⁴)

P = (x^3/2)/ y⁴