What is the answer to 2log_{5}(x)=log_{x}(25) ?

The answer to 2log_{5}(x)=log_{x}(25) is x=5,x= 1/5

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2log_{5}(x)=log_{x}(25)

2 lo g_{5} (x) = lo g_{x} (25)

x = 5, x = \frac{1}{5}

Decimal Notation

x = 5, x = 0.2

Solution steps

2 lo g_{5} (x) = lo g_{x} (25)

Apply log rules

2 lo g_{5} (x) = \frac{2}{lo g _{5} ( x )}

Rewrite the equation with

lo g_{5} (x) = u

2 u = \frac{2}{u}

Solve

2 u = \frac{2}{u} : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 1 : x = 5

Solve

lo g_{5} (x) = - 1 : x = \frac{1}{5}

x = 5, x = \frac{1}{5}

Verify Solutions:

x = 5

True

, x = \frac{1}{5}

True

The solutions are

x = 5, x = \frac{1}{5}

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

lo g_{3} (4 x - 1) = 4

e \cdot ln (x - 10) = e \cdot ln (8)

- 2 lo g_{4} (- 2 x + 3) - 5 = 5

10 lo g_{10} (x) = 36.3

What is the answer to 2log_{5}(x)=log_{x}(25) ?
The answer to 2log_{5}(x)=log_{x}(25) is x=5,x= 1/5
Solve for x: 2log_{5}(x)=log_{x}(25)
The solution is x=5,x= 1/5