Question

Solve the following simultaneous equations:

5logx 16 – 2log9 y = 19
3logx 16 + 4log9 y = 14
URGENT

Answer 1

x = 2

y = 3

Step-by-step explanation:

`5log_x16-2log_9Y=19\ \ --->Equation\ 1\\\\3log_x16+4log_9Y=14\ \ --->Equation\ 2\\`

Take e\Equation 1

`5log_x16-2log_9Y=19\\`

`5log_x16=19+2log_9Y\\\\log_x16=(19+2log_9Y)/(5) --->Equation\ 3`

Put Equation 3 in Equation 2

`3log_x16+4log_9Y=14\\\\3((19+2log_9Y)/(5))+4log_9Y=14 \\\\(57+6log_9Y)/(5)+4log_9Y=14\\\\(57+6log_9Y+20log_9Y)/(5) =14`

`57+6log_9Y+20log_9Y=70\\\\26log_9Y=70-57\\\\26log_9Y=13\\\\log_9Y=0.5\\\\y=3\\`

We got the value of y = 3 now insert y = 3 in Equation 3

`log_x16=(19+2log_9Y)/(5) \\\\log_x16=(19+2log_93)/(5) \\\\log_x16=(19+log_93^2)/(5) \\\\log_x16=(19+log_99)/(5) \\\\log_x16=(19+1)/(5) \\\\log_x16=4`

`x =2`

So we got x =2 and y =3