Question

(iv) 2^ 3x = 8^4x+3​

Answer 1

Step-by-step explanation:

Equalize base of both expressions

${2}^{3x} = {2}^{3(4x + 3)} \\ \\ {2}^{3x} = {2}^{12x + 9}$

Since base is same their power will be same

3x = 12x+9

3x-12x = 9

-9x = 9

x = -9/9

x = -1

Answer 2

Answer:

2^(3x) = 8^(4x + 3)

2^(3x) = 2^3^(4x + 3)

2^(3x) = 2^ {3 (4x + 3)}

since ,base are same both sides, then power should be equal.

3x = 3 (4x + 3)

3x = 12x + 9

3x - 12x = 9

-9x = 9

x = 9/(-9) = -1

FORMULA USED

x^m = x^n, then m equal to n ; m = n

Assumed

^n = power n

To check answer x = -1

put the value of x= -1 in given Question

2^(3x) = 8^(4x + 3)

2^3 (-1) = 8^{4 (-1) + 3 }

2^-3 = 8^(-4 + 3) since, y ^-1 = 1/y

1/8 = 8^(-1)

1/8 = 1/8

proved

hence , x = -1 is correct answer.

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