How to Solve a Logarithmic Practice Problem?
Solve the logarithmic practice problem
log x/(y – z) = log y/(z – x) = log z/(x – y) then find the value of xx yy zz
Solution to the logarithmic practice problem
Let, log x/(y – z) = log y/(z – x) = log z/(x – y) = k
log x/(y – z) = k
⇒ log x = k(y – z)
Multiply with x
x log x = kx(y – z)
⇒ log xx = kxy – kxz……………eq(1)
log y/(z – x) = k
⇒ log y = k(z – x)
Multiply with y
y log y = ky(z – x)
⇒ log yy = kyz – kxy……………eq(2)
log z/(x – y) = k
⇒ log z = k(x – y)
Multiply with z
z log z = kz(x – y)
⇒ log zz = kxz – kyz……………eq(3)
Add equation 1, equation 2 and equation 3, then
log xx+ log yy + log zz = kxy – kxz + kyz – kxy + kxz – kyz
⇒ log (xx . yy . zz) = 0
⇒ xx yy zz = 100
⇒ xx yy zz = 1
