What is the answer to 4^{x-2}=4^x-4^2 ?

The answer to 4^{x-2}=4^x-4^2 is x=(ln(16/15))/(2ln(2))+2

Solve for x: 4^{x-2}=4^x-4^2

The solution is x=(ln(16/15))/(2ln(2))+2

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

x = \frac{ln ( \frac{16}{15} )}{2 ln ( 2 )} + 2

Decimal Notation

x = 2.04655 \dots

Solution steps

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

Subtract

4^{x}

from both sides

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

Simplify

4^{x - 2} - 4^{x} = - 16

Factor

4^{x - 2} - 4^{x} : - 15 \cdot 4^{x - 2}

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

Divide both sides by

- 15

4^{x - 2} = \frac{16}{15}

Apply exponent rules

(x - 2) ln (4) = ln (\frac{16}{15})

Solve

(x - 2) ln (4) = ln (\frac{16}{15}) : x = \frac{ln ( \frac{16}{15} )}{2 ln ( 2 )} + 2

x = \frac{ln ( \frac{16}{15} )}{2 ln ( 2 )} + 2

5^{x - 2} = 1

2^{x - 1} + 3 = 7

2^{x} - 2 + 2^{- x} = 0

5^{x} = 11

y, x = 2^{- y}

What is the answer to 4^{x-2}=4^x-4^2 ?
The answer to 4^{x-2}=4^x-4^2 is x=(ln(16/15))/(2ln(2))+2
Solve for x: 4^{x-2}=4^x-4^2
The solution is x=(ln(16/15))/(2ln(2))+2