What is the answer to 3(2^{2x})-10(2^x)+8=0 ?

The answer to 3(2^{2x})-10(2^x)+8=0 is x=1,x=(ln(4/3))/(ln(2))

Solve for x: 3(2^{2x})-10(2^x)+8=0

The solution is x=1,x=(ln(4/3))/(ln(2))

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3 (2^{2 x}) - 10 (2^{x}) + 8 = 0

x = 1, x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}

Solution steps

3 (2^{2 x}) - 10 (2^{x}) + 8 = 0

Apply exponent rules

3 (2^{x})^{2} - 10 \cdot 2^{x} + 8 = 0

Rewrite the equation with

2^{x} = u

3 (u)^{2} - 10 u + 8 = 0

Solve

3 u^{2} - 10 u + 8 = 0 : u = 2, u = \frac{4}{3}

u = 2, u = \frac{4}{3}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 2 : x = 1

Solve

2^{x} = \frac{4}{3} : x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}

x = 1, x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}

4 \cdot 2^{5 x} = 64

8^{x + 1} = 2^{2 x + 5}

2^{x + 1} = 3^{x - 1}

(\frac{1}{5})^{3 x} = 125

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

What is the answer to 3(2^{2x})-10(2^x)+8=0 ?
The answer to 3(2^{2x})-10(2^x)+8=0 is x=1,x=(ln(4/3))/(ln(2))
Solve for x: 3(2^{2x})-10(2^x)+8=0
The solution is x=1,x=(ln(4/3))/(ln(2))