(c) 7^X+1 + 7^1 -x= 50
Answers
Step-by-step explanation:
Given :-
7^(X+1) + 7^(1-X) = 50
To find :-
Solve for X ?
Solution :-
Given equation is 7^(X+1) + 7^(1-X) = 50
We know that
a^m × a^n = a^(m+n)
a^m / a^n = a^(m-n)
=> (7^X × 7¹ )+ (7^X / 7¹) = 50
=> (7^X × 7 )+ (7^X / 7) = 50
=> 7^X [ 7+(1/7)] = 50
=> 7^X [ (49+1)/7] = 50
=> 7^X × (50/7) = 50
=>50× 7^X / 7 = 50
=> 50×7^X = 50×7
=> 7^X = 50×7/50
=> 7^X = 7
=> 7^X = 7¹
Since bases are equal then exponents must be equal
=> X = 1
Therefore,X = 1
Answer:-.
The value of X for the given problem is 1
Check:-
If X = 1 then
LHS = 7^(X+1) + 7^(1-X)
= 7^(1+1)+7^(1-1)
= 7²+7⁰
= 49+1
Since a⁰ = 1
= 50
= RHS
LHS = RHS is true for X = 1
Verified the given relations in the given problem
Used formulae:-
- a^m × a^n = a^(m+n)
- a^m /a^n = a^(m-n)
- a⁰ = 1
- If bases are equal then exponents must be equal.
- a^m = a^n => m=n
Answer:
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