What is the answer to 2^{3x}-2^x=120 ?

The answer to 2^{3x}-2^x=120 is x=(ln(5))/(ln(2))

Solve for x: 2^{3x}-2^x=120

The solution is x=(ln(5))/(ln(2))

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2^{3 x} - 2^{x} = 120

x = \frac{ln ( 5 )}{ln ( 2 )}

Decimal Notation

x = 2.32192 \dots

Solution steps

2^{3 x} - 2^{x} = 120

Apply exponent rules

(2^{x})^{3} - 2^{x} = 120

Rewrite the equation with

2^{x} = u

(u)^{3} - u = 120

Solve

u^{3} - u = 120 : u = 5

u = 5

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 5 : x = \frac{ln ( 5 )}{ln ( 2 )}

x = \frac{ln ( 5 )}{ln ( 2 )}

4 9^{x} - 6 \cdot 7^{x} - 7 = 0

8 1^{2 x + 3} = 9^{3 x + 1}

2^{2 x - 1} = 8

2^{n} = 64

- 10 e^{- x} = 0

What is the answer to 2^{3x}-2^x=120 ?
The answer to 2^{3x}-2^x=120 is x=(ln(5))/(ln(2))
Solve for x: 2^{3x}-2^x=120
The solution is x=(ln(5))/(ln(2))