What is the answer to 4^{x+2}+4^{x-1}= 65/64 ?

The answer to 4^{x+2}+4^{x-1}= 65/64 is x=-2

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4^{x+2}+4^{x-1}= 65/64

4^{x + 2} + 4^{x - 1} = \frac{65}{64}

x = - 2

Solution steps

4^{x + 2} + 4^{x - 1} = \frac{65}{64}

Factor

4^{x + 2} + 4^{x - 1} : 65 \cdot 4^{x - 1}

65 \cdot 4^{x - 1} = \frac{65}{64}

Divide both sides by

65

4^{x - 1} = \frac{1}{64}

Apply exponent rules

x - 1 = - 3

Solve

x - 1 = - 3 : x = - 2

x = - 2

6^{2 x} = 7^{x + 4}

9^{x - 2} = 27

4^{3 x - 1} = 3 2^{- 4}

5^{x} = 8^{x}

1 + e^{x - 1} = 0

What is the answer to 4^{x+2}+4^{x-1}= 65/64 ?
The answer to 4^{x+2}+4^{x-1}= 65/64 is x=-2
Solve for x: 4^{x+2}+4^{x-1}= 65/64
The solution is x=-2