What is the answer to log_{2}(x)-log_{4}(2x-1)=1 ?

The answer to log_{2}(x)-log_{4}(2x-1)=1 is x=2(2+sqrt(3)),x=2(2-sqrt(3))

Solve for x: log_{2}(x)-log_{4}(2x-1)=1

The solution is x=2(2+sqrt(3)),x=2(2-sqrt(3))

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lo g_{2} (x) - lo g_{4} (2 x - 1) = 1

x = 2 (2 + 3), x = 2 (2 - 3)

Decimal Notation

x = 7.46410 \dots, x = 0.53589 \dots

Solution steps

lo g_{2} (x) - lo g_{4} (2 x - 1) = 1

Apply log rules

x^{2} = 4 (2 x - 1)

Solve

x^{2} = 4 (2 x - 1) : x = 2 (2 + 3), x = 2 (2 - 3)

x = 2 (2 + 3), x = 2 (2 - 3)

Verify Solutions:

x = 2 (2 + 3)

True

, x = 2 (2 - 3)

True

The solutions are

x = 2 (2 + 3), x = 2 (2 - 3)

x, ln (y) + y = x + ln (x) + c

lo g_{2} (3 x - 2) = 1 + lo g_{2} (5)

x, ln (x) = - 2.27

lo g_{e} (x) = 4.57

ln (x^{2} - 3 x) = 0

What is the answer to log_{2}(x)-log_{4}(2x-1)=1 ?
The answer to log_{2}(x)-log_{4}(2x-1)=1 is x=2(2+sqrt(3)),x=2(2-sqrt(3))
Solve for x: log_{2}(x)-log_{4}(2x-1)=1
The solution is x=2(2+sqrt(3)),x=2(2-sqrt(3))