Question

If log (2x×3y) =log (288) then find the value of x,y

Answer 1

Answer:

the individual value of the x and y will not be unique but

the condition of xy =48 will always be hold true

Answer 2

x = 5 and y = 5

Step-by-step explanation:

We have,

$\log(2^x\times3^y) =\log(288)$

To find, the values of x and y = ?

∴ $\log(2^x\times3^y) =\log(288)$    

⇒ $2^x\times 3^y=288$

⇒ $2^x\times 3^y=2\times 2\times 2\times 2\times 2\times 3\times 3$

⇒ $2^x\times 3^y=2^5\times 3^2$

Equating the powers of 2 and 3 both sides, we get

$2^x=2^{5}$ and $3^y=3^{2}$

⇒ $2^x=2^{5}$

⇒ x = 5

and

$3^y=3^{2}$

⇒ y = 2

∴ x = 5 and y = 2

Thus, x = 5 and y = 2