Question

If log₁₀ x = a, log₁₀ y = b, If log₁₀ c = 2a – b, find c in terms of x and y.

Answer 1

Given: log₁₀ x = a, log₁₀ y = b

Step-wise calculation:

log₁₀ c = 2a − b

⇒ `c = 10^(2a - b)`

`10^(2a - b) = 10^(2a)/10^b `

`10^(2a - b) = (10^a)^2/10^b`

`10^(2a - b) = x^2/y`

`c = x^2/y`