SOLUTION: 2 log x base 5 + 3 log y base 3 = 8 6 log x base 5 - 2 log y base 3 = 2

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 2 log x base 5 + 3 log y base 3 = 8 6 log x base 5 - 2 log y base 3 = 2       Log On


   

Question 1168571: 2 log x base 5 + 3 log y base 3 = 8
6 log x base 5 - 2 log y base 3 = 2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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2 log x base 5 + 3 log y base 3 = 8
6 log x base 5 - 2 log y base 3 = 2
:
2%2Alog%285%2C%28x%29%29+%2B+3%2Alog%283%2C%28y%29%29+=+8
6%2Alog%285%2C%28x%29%29+-+2%2Alog%283%2C%28y%29%29+=+2
:
Multiply the first equation by 3, subtract the 2nd equation
6%2Alog%285%2C%28x%29%29+%2B+9%2Alog%283%2C%28y%29%29+=+24
6%2Alog%285%2C%28x%29%29+-+2%2Alog%283%2C%28y%29%29+=+2
-----------------------------------------Subtraction eliminate the 1st term
0+%2B+11%2Alog%283%2C%28y%29%29+=+22
divide both sides by 11
log%283%2C%28y%29%29+=+2
the exponent equiv of logs
y+=+3%5E2
y = 9
then find x
2%2Alog%285%2C%28x%29%29+%2B+3%2Alog%283%2C%289%29%29+=+8
we know that log%283%2C%289%29%29 = 2
2%2Alog%285%2C%28x%29%29+%2B+3%2A2+=+8
2%2Alog%285%2C%28x%29%29+=+8-6
2%2Alog%285%2C%28x%29%29+=+2
divide both sides by 2
log%285%2C%28x%29%29+=+1
exponent equiv of logs
x = 5