If 1960 = 2^a × 5^b × 7^c, find the values of a, b, c. Hence, calculate the value of 2^-a × 5^-c × 7^b

Given,

1960 = 2^a × 5^b × 7^c

Factorizing 1960, we get :

⇒ 1960 = 2³ × 5¹ × 7²

Equating the exponents,

⇒ 2³ × 5¹ × 7² = 2^a × 5^b × 7^c

⇒ a = 3, b = 1, c = 2.

The value of 2^-a × 5^-c × 7^b,

$\Rightarrow \dfrac{1}{2^a} \times \dfrac{1}{5^c} \times 7^b \\[1em] \Rightarrow \dfrac{1}{2^3} \times \dfrac{1}{5^2} \times 7^1 \\[1em] \Rightarrow \dfrac{1}{8} \times \dfrac{1}{25} \times 7^1 \\[1em] \Rightarrow \dfrac{7}{200}.$

Hence, a = 3, b = 1, c = 2 and 2^-a × 5^-c × 7^b = $\dfrac{7}{200}$.

Solve for x: