What is the answer to 7^{2x}-48(7^x)-49=0 ?

The answer to 7^{2x}-48(7^x)-49=0 is x=2

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7^{2x}-48(7^x)-49=0

7^{2 x} - 48 (7^{x}) - 49 = 0

x = 2

Solution steps

7^{2 x} - 48 (7^{x}) - 49 = 0

Apply exponent rules

(7^{x})^{2} - 48 \cdot 7^{x} - 49 = 0

Rewrite the equation with

7^{x} = u

(u)^{2} - 48 u - 49 = 0

Solve

u^{2} - 48 u - 49 = 0 : u = 49, u = - 1

u = 49, u = - 1

Substitute back

u = 7^{x},

solve for

x

Solve

7^{x} = 49 : x = 2

Solve

7^{x} = - 1 :

No Solution for

x \in R

x = 2

8 1^{x - 1} = 3^{8}

16 \cdot 4^{x - 2} = 8^{x^{2} - x}

4 (1.2)^{x} = 36

e^{3 x + 2} = 1

2^{x + 1} = 256

What is the answer to 7^{2x}-48(7^x)-49=0 ?
The answer to 7^{2x}-48(7^x)-49=0 is x=2
Solve for x: 7^{2x}-48(7^x)-49=0
The solution is x=2