What is the answer to 4^{n+1}=512+2^{2n-1} ?

The answer to 4^{n+1}=512+2^{2n-1} is n=(ln(1024/7))/(2ln(2))

Solve for n: 4^{n+1}=512+2^{2n-1}

The solution is n=(ln(1024/7))/(2ln(2))

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4^{n + 1} = 512 + 2^{2 n - 1}

n = \frac{ln ( \frac{1024}{7} )}{2 ln ( 2 )}

Decimal Notation

n = 3.59632 \dots

Solution steps

4^{n + 1} = 512 + 2^{2 n - 1}

Apply exponent rules

2 n ln (2) = ln (\frac{1024}{7})

Solve

2 n ln (2) = ln (\frac{1024}{7}) : n = \frac{ln ( \frac{1024}{7} )}{2 ln ( 2 )}

n = \frac{ln ( \frac{1024}{7} )}{2 ln ( 2 )}

2 5^{7} = 5^{x}

2^{r} = 100

3^{x + 1} = 7

2^{4} \cdot (0.5)^{- 3} = 2^{k}

e^{x} \cdot (x - 1) = 0

What is the answer to 4^{n+1}=512+2^{2n-1} ?
The answer to 4^{n+1}=512+2^{2n-1} is n=(ln(1024/7))/(2ln(2))
Solve for n: 4^{n+1}=512+2^{2n-1}
The solution is n=(ln(1024/7))/(2ln(2))