What is the answer to log_{2}(6*2^{2n+1}-6)=n ?

The answer to log_{2}(6*2^{2n+1}-6)=n is n=(ln(3/4))/(ln(2))

Solve for n: log_{2}(6*2^{2n+1}-6)=n

The solution is n=(ln(3/4))/(ln(2))

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lo g_{2} (6 \cdot 2^{2 n + 1} - 6) = n

n = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

Decimal

n = - 0.41503 \dots

Solution steps

lo g_{2} (6 \cdot 2^{2 n + 1} - 6) = n

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

2^{l o g_{2} (6 \cdot 2^{2 n + 1} - 6)} = 2^{n}

Simplify

2^{l o g_{2} (6 \cdot 2^{2 n + 1} - 6)} : 3 \cdot 2^{2 n + 2} - 6

3 \cdot 2^{2 n + 2} - 6 = 2^{n}

Solve

3 \cdot 2^{2 n + 2} - 6 = 2^{n} : n = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

n = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

Verify Solutions:

n = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

True

The solution is

n = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

lo g_{10} (x) - lo g_{10} (9) = 1

6.7 = lo g_{10} (\frac{I}{1})

lo g_{9} (x) = 5

lo g_{10} (- \frac{1}{3} x) + 1 = 0

25 = 20 lo g_{10} (x)

What is the answer to log_{2}(6*2^{2n+1}-6)=n ?
The answer to log_{2}(6*2^{2n+1}-6)=n is n=(ln(3/4))/(ln(2))
Solve for n: log_{2}(6*2^{2n+1}-6)=n
The solution is n=(ln(3/4))/(ln(2))