Question

Given log₁₀x = 2a and log₁₀y = `b/2. "If"  log_10^p = 3a - 2b`, express P in terms of x and y.

Answer 1

We know 10^a = x^1/2
10^b/2 = y
⇒ 10^b = y² 
`log_10^p` = 3a - 2b
⇒  p = 10^{3a - 2b}
⇒  p = (10³)^a ÷  (10²)^b
⇒  p = ( 10a )³ ÷ ( 10^b )² 
Substituting 10^a & 10^b, We get
⇒ p = ( x^1/2 )³ ÷ ( y² )²

⇒ p = `x^(3/2) ÷  y^4`

⇒ p = `x^(3/2)/y^4`