Question

Solve the following equations for x and y:
log₁₀(xy) = 2, log₁₀(x/y) + 2 log₁₀ 2 = 2

Answer 1

Answer:

this is not social it's is math

Answer 2

x= 50, y = 2

Explanation:

Given log₁₀(xy) = 2

log x + log y = 2  

log x = 2- log y-----(1)

Given log₁₀(x/y) + 2 log₁₀ 2 = 2

log x - log y + 2 log 2 = 2 -------(2)

Substituting (1) in (2), we get:

2- log y - log y + 2 log 2 = 2

-2 log y = -2 log 2

-2 will get cancelled on both sides.

log y = log 2.

So y = 2.

Given log₁₀(xy) = 2

Substituting y = 2, we get log2x = 2.

Common logarithm of 100 is 2, so we write the right-hand side as log 100.

log2x = log100

So 2x = 100, hence x = 50