What is the answer to 7^{n+2}+49^{n+1}=120050 ?

The answer to 7^{n+2}+49^{n+1}=120050 is n=2

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7^{n+2}+49^{n+1}=120050

7^{n + 2} + 4 9^{n + 1} = 120050

n = 2

Solution steps

7^{n + 2} + 4 9^{n + 1} = 120050

Apply exponent rules

7^{n} \cdot 7^{2} + (7^{n})^{2} \cdot 7^{2} = 120050

Rewrite the equation with

7^{n} = u

u \cdot 7^{2} + (u)^{2} \cdot 7^{2} = 120050

Solve

u \cdot 7^{2} + u^{2} \cdot 7^{2} = 120050 : u = 49, u = - 50

u = 49, u = - 50

Substitute back

u = 7^{n},

solve for

n

Solve

7^{n} = 49 : n = 2

Solve

7^{n} = - 50 :

No Solution for

n \in R

n = 2

2^{x^{2}} = 4^{\frac{9}{2} x - 9}

1 7^{- 2 x} = 6^{- x - 2}

2 5^{\frac{1}{2} + 2 x} = 5

7^{x^{2} - 5 x + 6} = 1

5^{x^{2} - 7 x + 9} = \frac{1}{125}

What is the answer to 7^{n+2}+49^{n+1}=120050 ?
The answer to 7^{n+2}+49^{n+1}=120050 is n=2
Solve for n: 7^{n+2}+49^{n+1}=120050
The solution is n=2