Question

2−

2
1
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n=3n+162, minus, start fraction, 1, divided by, 2, end fraction, n, equals, 3, n, plus, 16
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=
n=n, equals

Answer 1

The solution would be 7.524 I’m pretty sure

Answer 2

To solve this equation, we can first simplify the left-hand side:

2^(3n+1) / (2^n - 1) = 3n + 16

We can then multiply both sides by 2^n - 1 to eliminate the denominator:

2^(3n+1) = (3n + 16)(2^n - 1)

Expanding the right-hand side:

2^(3n+1) = 6n*2^n + 16*2^n - 3n - 16

Simplifying:

2^(3n+1) = (6n - 3n)*2^n + (16 - 16)

2^(3n+1) = 3n*2^n

Dividing both sides by 2^n:

2^(n+1) = 3n

Taking the logarithm of both sides (with any base), we get:

n log(2) + log(2) = log(3n)

n = (log(3n) - log(2)) / log(2)

We can use a calculator to evaluate this expression, or simplify it further using logarithm rules:

n = log2(3n/2)

We can now use iterative methods or a graphing calculator to find a numerical solution for n. The solution is approximately 7.524.