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

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

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

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

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

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

Decimal

x = - 0.41503 \dots

Solution steps

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

f (x) = g (x),

then

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

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

Simplify

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

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

Solve

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

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

Verify Solutions:

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

True

The solution is

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

lo g_{10} (3 x + 1) - lo g_{10} (2 x - 3) = 10

lo g_{0.5} (x) = 4

- 20 = lo g_{10} (x)

3 ln (x) = 12

lo g_{2} (x) = lo g_{2} (x)

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