Question

Solve the following simultaneous equations:
5logx 16 – 2log9 y = 19
3logx 16 + 4log9 y = 14
URGENT

Answer 1

Answer:

x = 2

y = 3

Explanation:

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

Take e\Equation 1

$5log_x16-2log_9Y=19$

$5log_x16=19+2log_9Y\\\\log_x16=\frac{19+2log_9Y}{5} --->Equation\ 3$

Put Equation 3 in Equation 2

$3log_x16+4log_9Y=14\\\\3(\frac{19+2log_9Y}{5})+4log_9Y=14 \\\\\frac{57+6log_9Y}{5}+4log_9Y=14\\\\\frac{57+6log_9Y+20log_9Y}{5} =14$

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

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

$log_x16=\frac{19+2log_9Y}{5} \\\\log_x16=\frac{19+2log_93}{5} \\\\log_x16=\frac{19+log_93^2}{5} \\\\log_x16=\frac{19+log_99}{5} \\\\log_x16=\frac{19+1}{5} \\\\log_x16=4$

$x =2$

So we got x =2 and y =3