Question

plzz answer no i in the following image through indices

Answer 1

1) 2^x.6^y = 24

2^x (2×3)^y = 24

[ (xy)^m = x^m.y^m use here]

2^(x + y).3^y = 2 × 2 × 2 × 3

2^(x + y).3^y = 2³ .3¹
this is only possible when ,
2^(x + y) = 2³ and 3^y = 3¹

hence,

(x + y) = 3
y = 1

so, x = 2 and y = 1

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(2)
2^2x.3^y = 48

2^2x .3^y = 2 × 2 × 2 × 2 × 3

2^2x .3^y = 2⁴ .3¹
this is possible when ,
2^2x = 2⁴ and 3^y = 3¹

2x = 4 and y = 1

hence , x = 2 and y = 1