Solve the system of equations logy x 3 logy4x5Solutionlogy

Solve the system of equations

log_y x = 3

log_y(4x)=5

Solution

logy x = 3
(log x)/(log y) = 3

logy(4x)=5
log (4x)/(log y) = 5
(log 4 + log x)/log y = 5
(log 4 / log y) + (log x / log y) = 5
from 1st equation (log x / log y) = 3
so,
(log 4 / log y) +3 = 5
(log 4 / log y) = 2
log y = (log 4)/ 2
log y = (log 2^2)/ 2
log y = 2*(log 2)/ 2
log y = log 2
y = 2

we have
log x/ log y = 3
log x = 3*log 2
log x = log (2^3)
log x = log 8
x = 8
Answer:
x=8 and y=2