Question

2logxbase5 3logybase3=8
and
6logxbase5 2logybase3=2
solve silmultaneously

Answer 1

`2\log_5{x}+3\log_3{y}=8 \ . \ . \ . \ (1)\\6\log_5{x}+2\log_3{y}=2 \ . \ . \ . \ (2)\\ \\ (1)*3:6\log_5{x}+9\log_3{y}=24 \ . \ . \ . \ (3) \\ \\ (3)-(2):7\log_3{y}=22\\ \log_3y=(22)/(7)\\3^(\log_3y)=3^{(22)/(7)}=31.59\\y=31.59\\ \\ From \ (1), 2\log_5{x}+3\log_3{31.59}=8\\2\log_5{x}=8-9.429=-1.429\\ \log_5{x}= -(1.429)/(2) =-0.7143\\5^{\log_5{x}}=5^(-0.7143)\\x=0.3168`

Therefore, x = 0.3168 and y = 31.59