What is the answer to 5^x+3*5^{x-2}=140 ?

The answer to 5^x+3*5^{x-2}=140 is x=3

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5^x+3*5^{x-2}=140

5^{x} + 3 \cdot 5^{x - 2} = 140

x = 3

Solution steps

5^{x} + 3 \cdot 5^{x - 2} = 140

Factor

5^{x} + 3 \cdot 5^{x - 2} : 28 \cdot 5^{x - 2}

28 \cdot 5^{x - 2} = 140

Divide both sides by

28

5^{x - 2} = 5

Apply exponent rules

x - 2 = 1

Solve

x - 2 = 1 : x = 3

x = 3

(3^{x + 1}) (4^{x + 2}) = (5^{x + 3})

8^{x + 4} = 16

x^{2 x} = 16

4^{x + 2} \cdot 8^{3 x + 1} = 64

1 0^{x} = 45

What is the answer to 5^x+3*5^{x-2}=140 ?
The answer to 5^x+3*5^{x-2}=140 is x=3
Solve for x: 5^x+3*5^{x-2}=140
The solution is x=3