Asked by samson

2logxbase5+3logybase3=8
and
6logxbase5+2logybase3=2
solve silmultaneously
Answered by Steve
just for ease of readability, let's say

u = log<sub><sub>5</sub></sub>x
v = log<sub><sub>3</sub></sub>y

Then we have

2u+3v=8
6u+2v=2

This has the solution
u = -5/7
v = 22/7
Unusual for a problem of this kind, but anyway...

log<sub><sub>5</sub></sub>x = -5/7, so x = 5^(-5/7)
log<sub><sub>3</sub></sub>y = 22/7, so y = 3^(22/7)
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