Question

the value of x such that(3/7)³× (3/7)‐⁸ = (3/7)2x+3​

Answer 1

Answer:

x= 4

Step-by-step explanation:

$( { \frac{3}{7} })^{3} \times { \frac{3}{7} }^{8} = { \frac{3}{7} }^{2x + 3} \\ { \frac{3}{7} }^{11} = { \frac{3}{7} }^{2x + 3} \\ 2x + 3 = 11 \\ 2x = 11 - 3 \\ 2x =8 \\ x = \frac{8}{2} = 4$

Answer 2

Step-by-step explanation:

Given Question:-

the value of x such that(3/7)³× (3/7)‐⁸ = (3/7)2x+3

Correct Question:-

Find the value of x such that

(3/7)^3 × (3/7)^-8 = (3/7)^(2x+3)

Solution:-

Given that

(3/7)^3 × (3/7)^-8 = (3/7)^(2x+3)

LHS is in the form of a^m × a^n

Where a = 3/7 and m = 3 and n = -8

We know that

a^m × a^n = a^(m+n)

=> (3/7)^(3+(-8)) = (3/7)^(2x+3)

=> (3/7)^(3-8) = (3/7)^(2x+3)

=> (3/7)^-5 = (3/7)^(2x+3)

On Comparing both sides then

=> -5 = 2x+3

=> 2x+3 = -5

=> 2x = -5-3

=>2x = -8

=> x = -8/2

=> x = -4

Therefore, x = -4

Answer:-

The value of x for the given problem is-4

Check:-

If x = -4 then

LHS:-

(3/7)^3 × (3/7)^-8

=> (3/7)^3-8

=> (3/7)^-5

RHS:-

(3/7)^(2×-4+3)

=> (3/7)^(-8+3)

=> (3/7)-5

LHS = RHS is true for x = -4

Used formula:-

• a^m × a^n = a^(m+n)