Question

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

Answer 1

Step-by-step explanation:

Log(2x ×3y) = log(288)

Log(6xy) = log(288)

taking anti log on both sides we get

6xy = 288

xy= 48

Therefore, there would be multiple values of x and y whose product is 48 one of them could be 6 and 8 or 24 and 2, etc.

Answer 2

x = 5 and y = 2

Step-by-step explanation:

We have,

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

To find, the value 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

Hence, x = 5 and y = 2