Question

49 into 7 to the power x is equal to 343 to the power 1 by 3

Answer 1

The value of x is "- 1".

Step-by-step explanation:

We have,

$49\times 7^{x} =343^{\dfrac{1}{3} }$

To find, the value of x = ?

∴ $49\times 7^{x} =343^{\dfrac{1}{3}}$

⇒ $7^{2} \times 7^{x} =(7^{3} )^{\dfrac{1}{3}}$

⇒ $7^{2+x} =(7^{3\times \dfrac{1}{3}})$

[ ∵ $a^{m} \times a^{n} =a^{m+n} and (a^{m} )^{n} =a^{mn}$]

⇒ $7^{2+x} =7^{1}$

Equating the power of 7, we get

∴ 2 + x = 1

⇒ x = 1 - 2 = - 1

Hence, the value of x is "- 1".

Answer 2

Answer:

x=-1

Step-by-step explanation:

49×7^x=(343)1/3

=>7^2×7^x=7^3×1/3

=>7^2+x=7^1

On solving power of 7 we get,

2+x=1

x=1-2

x=-1