Question

5^2x-y=625
2^x-y=5. Find x and y

Answer 1

Answer:

We have

${5}^{2x} - y = 625$

And

${2}^{x} - y = 5$

Subtracting 2nd from ist, we have

${5}^{2x} - y - {2}^{x} + y = 625 - 5$

${5}^{2x} - {2}^{x} = 620$

Apply

$log \: on \: both \: sides$

$log( {5}^{2x} - {2}^{x} ) = log(620)$

$\frac{ log( {5}^{2x} ) }{ log( {2}^{x} ) } = 2.7924$

$\frac{2x log(5) }{x log(2) } = 2.7924$

$\frac{2x \times 0.699}{x \times 0.3010} = 2.7924$

$\frac{1.869x}{0.3010x} = 2.7924$

$1.869x = 0.8405x$

$1.0285x = 0$

$x = 0$

Put x=o in ist equation

$y = - 624$