What is the answer to x^{2log_{x}(x+1)}=5x-1 ?

The answer to x^{2log_{x}(x+1)}=5x-1 is x=2

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x^{2log_{x}(x+1)}=5x-1

x^{2 l o g_{x} (x + 1)} = 5 x - 1

x = 2

Solution steps

x^{2 l o g_{x} (x + 1)} = 5 x - 1

Apply log rules

(x + 1)^{2} = 5 x - 1

Solve

(x + 1)^{2} = 5 x - 1 : x = 2, x = 1

x = 2, x = 1

Verify Solutions:

x = 2

True

, x = 1

False

The solution is

x = 2

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

ln (2 x - 3) = 0

ln (2 x - 3) = 4

ln (3 x - 7) = 2

2 lo g_{10} (x) = lo g_{10} (2 x)

What is the answer to x^{2log_{x}(x+1)}=5x-1 ?
The answer to x^{2log_{x}(x+1)}=5x-1 is x=2
Solve for x: x^{2log_{x}(x+1)}=5x-1
The solution is x=2