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

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

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

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

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

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

Decimal Notation

x = 0.04655 \dots

Solution steps

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

Subtract

4^{x + 2}

from both sides

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

Simplify

4^{x} + 16 - 4^{x + 2} = 0

Factor

4^{x} + 16 - 4^{x + 2} : - 15 \cdot 4^{x} + 16

- 15 \cdot 4^{x} + 16 = 0

Add

15 \cdot 4^{x}

to both sides

- 15 \cdot 4^{x} + 16 + 15 \cdot 4^{x} = 0 + 15 \cdot 4^{x}

Simplify

16 = 15 \cdot 4^{x}

Switch sides

15 \cdot 4^{x} = 16

Divide both sides by

15

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

Apply exponent rules

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

Solve

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

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

4^{x} + 48 = 19 \cdot 2^{x}

64 (4^{2 x}) - 20 (4^{x}) + 1 = 0

3 \cdot 9^{x} - 10 \cdot 3^{x} + 3 = 0

6^{x} = 23

x, 0 = e^{x y}

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