Question

find the x value and please solve on paper and keep photo please​

Answer 1

Step-by-step explanation:

Given :-

(8/9)^3 × (8/9)^-6 = (8/9)^(2x-1)

To find :-

Find the value of x ?

Solution :-

Given equation is (8/9)^3 × (8/9)^-6 = (8/9)^(2x-1)

=> (8/9)^(3-6) = (8/9)^(2x-1)

Since a^m × a^n = a^(m+n)

=> (8/9)^-3 = (8/9)^(2x-1)

We know that

If the bases are equal then exponents must be equal.

=> -3 = 2x-1

=> 2x-1 = -3

=> 2x = -3+1

=> 2x = -2

=> x = -2/2

=> x = -1

Answer:-

The value of x for the given problem is -1

Check:-

If x = -1 then

LHS = (8/9)^3 × (8/9)^-6

=>(8/9)^3-6

=> (8/9)^-3 ------(1)

RHS = (8/9)^(2×-1-1)

=> (8/9)^(-2-1)

=> (8/9)^-3-------(2)

LHS = RHS is true for x = -1

Used formulae:-

→ a^m × a^n = a^(m+n)

→If the bases are equal then exponents must be equal.