Question

To solve 493x = 3432x+1, write each side of the equation in terms of base .

Answer 1

Answer:

The value of x is (-1)/2939

Answer 2

Question :- To solve 49^3x = 343^(2x+1), write each side of the equation in terms of base . ?

Solution :-

→ 49^3x = 343^(2x+1)

→ (7²)^3x = (7³)^(2x + 1)

using (a^m)^n = a^(m * n) both sides,

→ (7)^(2 * 3x) = 7^{3 * (2x + 1)}

→ 7^(6x) = 7^(6x + 3)

now, when base is both sides is same , so, power will be equal .

→ 6x = 6x + 3

→ 6x - 6x = 3

→ 0 = 3 .

therefore, the equation has no solution .

_____________

Correct Question :- 49^3x = 343^(x+1)

→ 49^3x = 343^(2x+1)

→ (7²)^3x = (7³)^(x + 1)

→ (7)^(2 * 3x) = 7^{3 * (x + 1)}

→ 7^(6x) = 7^(3x + 3)

→ 6x = 3x + 3

→ 6x - 3x = 3

→ 3x = 3

→ x = 1 . (Ans.)

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