What is the answer to 3\times 2^{2x}-10(2)^x=0 ?

The answer to 3\times 2^{2x}-10(2)^x=0 is x=(ln(10)-ln(3))/(ln(2))

Solve for x: 3\times 2^{2x}-10(2)^x=0

The solution is x=(ln(10)-ln(3))/(ln(2))

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3 \cdot 2^{2 x} - 10 (2)^{x} = 0

x = \frac{ln ( 10 ) - ln ( 3 )}{ln ( 2 )}

Decimal Notation

x = 1.73696 \dots

Solution steps

3 \cdot 2^{2 x} - 10 (2)^{x} = 0

Add

10 \cdot 2^{x}

to both sides

3 \cdot 2^{2 x} - 10 \cdot 2^{x} + 10 \cdot 2^{x} = 0 + 10 \cdot 2^{x}

Simplify

3 \cdot 2^{2 x} = 10 \cdot 2^{x}

Apply exponent rules

ln (3) + 2 x ln (2) = ln (10) + x ln (2)

Solve

ln (3) + 2 x ln (2) = ln (10) + x ln (2) : x = \frac{ln ( 10 ) - ln ( 3 )}{ln ( 2 )}

x = \frac{ln ( 10 ) - ln ( 3 )}{ln ( 2 )}

1 6^{3 x - 3} = 6 4^{x + 3}

2^{2 + x} - 2^{2 - x} = 15

2^{3 - 2 x} = 8

3^{x^{2}} = 9^{x + 4}

9^{x - 5} = 1 2^{x}

What is the answer to 3\times 2^{2x}-10(2)^x=0 ?
The answer to 3\times 2^{2x}-10(2)^x=0 is x=(ln(10)-ln(3))/(ln(2))
Solve for x: 3\times 2^{2x}-10(2)^x=0
The solution is x=(ln(10)-ln(3))/(ln(2))