What is the answer to 5(2^{2p+1})-17(2^{p+3})=0 ?

The answer to 5(2^{2p+1})-17(2^{p+3})=0 is p=(ln(68/5))/(ln(2))

Solve for p: 5(2^{2p+1})-17(2^{p+3})=0

The solution is p=(ln(68/5))/(ln(2))

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5 (2^{2 p + 1}) - 17 (2^{p + 3}) = 0

p = \frac{ln ( \frac{68}{5} )}{ln ( 2 )}

Decimal Notation

p = 3.76553 \dots

Solution steps

5 (2^{2 p + 1}) - 17 (2^{p + 3}) = 0

Add

17 \cdot 2^{p + 3}

to both sides

5 \cdot 2^{2 p + 1} - 17 \cdot 2^{p + 3} + 17 \cdot 2^{p + 3} = 0 + 17 \cdot 2^{p + 3}

Simplify

5 \cdot 2^{2 p + 1} = 17 \cdot 2^{p + 3}

Apply exponent rules

ln (5) + (2 p + 1) ln (2) = ln (17) + (p + 3) ln (2)

Solve

ln (5) + (2 p + 1) ln (2) = ln (17) + (p + 3) ln (2) : p = \frac{ln ( \frac{68}{5} )}{ln ( 2 )}

p = \frac{ln ( \frac{68}{5} )}{ln ( 2 )}

2048 = 4 \cdot 2^{x}

5^{x} = \frac{6}{11}

5^{3 x - 2} = 40

2^{2 x - 1} - 5 \cdot 2^{x - 1} + 2 = 0

2. 4^{x} + 3 = 20

What is the answer to 5(2^{2p+1})-17(2^{p+3})=0 ?
The answer to 5(2^{2p+1})-17(2^{p+3})=0 is p=(ln(68/5))/(ln(2))
Solve for p: 5(2^{2p+1})-17(2^{p+3})=0
The solution is p=(ln(68/5))/(ln(2))