What is the answer to 4^{x-4}+4^{x-3}+4^{x-1}=276 ?

The answer to 4^{x-4}+4^{x-3}+4^{x-1}=276 is x=5

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4^{x-4}+4^{x-3}+4^{x-1}=276

4^{x - 4} + 4^{x - 3} + 4^{x - 1} = 276

x = 5

Solution steps

4^{x - 4} + 4^{x - 3} + 4^{x - 1} = 276

Factor

4^{x - 4} + 4^{x - 3} + 4^{x - 1} : 69 \cdot 4^{x - 4}

69 \cdot 4^{x - 4} = 276

Divide both sides by

69

4^{x - 4} = 4

Apply exponent rules

x - 4 = 1

Solve

x - 4 = 1 : x = 5

x = 5

5^{3 x} = 2 5^{(x - 1)}

3^{x} \cdot 5^{x + 1} = 125

9^{(4 x - 5)} = 2 5^{(6 x + 2)}

e^{3 x} = \frac{1}{64}

7^{x - 1} = 3^{x + 1}

What is the answer to 4^{x-4}+4^{x-3}+4^{x-1}=276 ?
The answer to 4^{x-4}+4^{x-3}+4^{x-1}=276 is x=5
Solve for x: 4^{x-4}+4^{x-3}+4^{x-1}=276
The solution is x=5