What is the answer to 5^{x-2}+5^{x+1}=126 ?

The answer to 5^{x-2}+5^{x+1}=126 is x=2

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5^{x-2}+5^{x+1}=126

5^{x - 2} + 5^{x + 1} = 126

x = 2

Solution steps

5^{x - 2} + 5^{x + 1} = 126

Factor

5^{x - 2} + 5^{x + 1} : 126 \cdot 5^{x - 2}

126 \cdot 5^{x - 2} = 126

Divide both sides by

126

5^{x - 2} = 1

Apply exponent rules

(x - 2) ln (5) = ln (1)

Solve

(x - 2) ln (5) = ln (1) : x = 2

x = 2

x, 4 e^{2 x} = 12

x, e^{6 - 4 x} = 3

e^{2 l n (x)} = 4

e^{2 x} = 25

2^{2 - x} = 8

What is the answer to 5^{x-2}+5^{x+1}=126 ?
The answer to 5^{x-2}+5^{x+1}=126 is x=2
Solve for x: 5^{x-2}+5^{x+1}=126
The solution is x=2