What is the answer to log_{4}(9x)-log_{2}(x-1)=2 ?

The answer to log_{4}(9x)-log_{2}(x-1)=2 is x=(41+3sqrt(73))/(32)

Solve for x: log_{4}(9x)-log_{2}(x-1)=2

The solution is x=(41+3sqrt(73))/(32)

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lo g_{4} (9 x) - lo g_{2} (x - 1) = 2

x = \frac{41 + 3 73}{32}

Decimal Notation

x = 2.08225 \dots

Solution steps

lo g_{4} (9 x) - lo g_{2} (x - 1) = 2

Apply log rules

9 x = 16 (x - 1)^{2}

Solve

9 x = 16 (x - 1)^{2} : x = \frac{41 + 3 73}{32}, x = \frac{41 - 3 73}{32}

x = \frac{41 + 3 73}{32}, x = \frac{41 - 3 73}{32}

Verify Solutions:

x = \frac{41 + 3 73}{32}

True

, x = \frac{41 - 3 73}{32}

False

The solution is

x = \frac{41 + 3 73}{32}

2 (x + 1) ln (x + 1) + (x + 1) = 0

3 lo g_{5} (y) - lo g_{y} (5) = 2

lo g_{4} (x + 3) = lo g_{4} (3 x - 7)

1 0^{7 l o g_{10} (x)} = 7 x

35000 = 95858 ln (x) - 991636

What is the answer to log_{4}(9x)-log_{2}(x-1)=2 ?
The answer to log_{4}(9x)-log_{2}(x-1)=2 is x=(41+3sqrt(73))/(32)
Solve for x: log_{4}(9x)-log_{2}(x-1)=2
The solution is x=(41+3sqrt(73))/(32)