What is the answer to 2^x+2^{x+2}+2^{x+4}=5370 ?

The answer to 2^x+2^{x+2}+2^{x+4}=5370 is x=(ln(1790/7))/(ln(2))

Solve for x: 2^x+2^{x+2}+2^{x+4}=5370

The solution is x=(ln(1790/7))/(ln(2))

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2^{x} + 2^{x + 2} + 2^{x + 4} = 5370

x = \frac{ln ( \frac{1790}{7} )}{ln ( 2 )}

Decimal Notation

x = 7.99838 \dots

Solution steps

2^{x} + 2^{x + 2} + 2^{x + 4} = 5370

Factor

2^{x} + 2^{x + 2} + 2^{x + 4} : 21 \cdot 2^{x}

21 \cdot 2^{x} = 5370

Divide both sides by

21

2^{x} = \frac{1790}{7}

Apply exponent rules

x ln (2) = ln (\frac{1790}{7})

Solve

x ln (2) = ln (\frac{1790}{7}) : x = \frac{ln ( \frac{1790}{7} )}{ln ( 2 )}

x = \frac{ln ( \frac{1790}{7} )}{ln ( 2 )}

10000 = 30000 (1 + 0.08)^{n}

1^{x} + 6^{x} + 8^{x} = 9^{x}

2^{x} + 4^{x} = 8^{x}

(\frac{1}{3})^{3 - 2 x} = 243

y, x (x + 2) (x + 8) = 3^{y}

What is the answer to 2^x+2^{x+2}+2^{x+4}=5370 ?
The answer to 2^x+2^{x+2}+2^{x+4}=5370 is x=(ln(1790/7))/(ln(2))
Solve for x: 2^x+2^{x+2}+2^{x+4}=5370
The solution is x=(ln(1790/7))/(ln(2))