Question 1168571
2 log x base 5 + 3 log y base 3 = 8
6 log x base 5 - 2 log y base 3 = 2
:
{{{2*log(5,(x)) + 3*log(3,(y)) = 8}}}
{{{6*log(5,(x)) - 2*log(3,(y)) = 2}}}
:
Multiply the first equation by 3, subtract the 2nd equation
{{{6*log(5,(x)) + 9*log(3,(y)) = 24}}}
{{{6*log(5,(x)) - 2*log(3,(y)) = 2}}}
-----------------------------------------Subtraction eliminate the 1st term
{{{0 + 11*log(3,(y)) = 22}}}
divide both sides by 11
{{{log(3,(y)) = 2}}}
the exponent equiv of logs
{{{y = 3^2}}}
y = 9
then find x
{{{2*log(5,(x)) + 3*log(3,(9)) = 8}}}
we know that {{{log(3,(9))}}} = 2
{{{2*log(5,(x)) + 3*2 = 8}}}
{{{2*log(5,(x)) = 8-6}}}
{{{2*log(5,(x)) = 2}}}
divide both sides by 2
{{{log(5,(x)) = 1}}}
exponent equiv of logs
x = 5