Find the number of integral pairs for $(x, y)$ from the following equations
${log}_{100} | x + y | = \frac{1}{2}$ and ${log}_{10} y - {log}_{10} | x | = {log}_{100} 4$

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $2$
$| x + y | = (100)^{1 / 2} | x + y | = 10 x + y = \pm 10$
${log}_{10} (\frac{y}{| x |}) = {log}_{10} 2 y = 2 | x | y = \pm 2 x$

$x + y = 10 y = 2 x 3 x = 10 x = \frac{10}{3}, y = \frac{20}{3}$

$x + y = 10 y = - 2 x - x = 10 x = - 10, y = 20$

$x + y = - 10 y = - 2 x - x = - 10 x = 10, y = - 20$

$x + y = - 10 y = 2 x 3 x = - 10 x = \frac{- 10}{3}, y = \frac{- 20}{3}$

Number of integer solutions: $(- 10, 20)$ and $(10, - 20) = 2$

Suggest Corrections

Similar questions

(x, y)

{log}_{100} | x + y | = \frac{1}{2}, {log}_{10} y - {log}_{10} | x | = {log}_{100} 4

{log}_{100} | x + y | = \frac{1}{2}, {log}_{10} y - {log}_{10} | x | = {log}_{100} 4

x

y

{log}_{100} | x + y | = \frac{1}{2}

{log}_{10} y - {log}_{10} | x | = {log}_{100} 4

(x, y)

x

y

{log}_{100} | x + y | = \frac{1}{2}, {log}_{10} y - {log}_{10} | x | = {log}_{100} 4

x

y

{log}_{100} | x + y | = \frac{1}{2}, {log}_{10} y - {log}_{10} | x | = {log}_{100} 4

Join BYJU'S Learning Program