What is the answer to log_{5}(x)+log_{x}(25)=3 ?

The answer to log_{5}(x)+log_{x}(25)=3 is x=25,x=5

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log_{5}(x)+log_{x}(25)=3

lo g_{5} (x) + lo g_{x} (25) = 3

x = 25, x = 5

Solution steps

lo g_{5} (x) + lo g_{x} (25) = 3

Apply log rules

lo g_{5} (x) + \frac{2}{lo g _{5} ( x )} = 3

Rewrite the equation with

lo g_{5} (x) = u

u + \frac{2}{u} = 3

Solve

u + \frac{2}{u} = 3 : u = 2, u = 1

u = 2, u = 1

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

Solve

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

x = 25, x = 5

Verify Solutions:

x = 25

True

, x = 5

True

The solutions are

x = 25, x = 5

lo g_{4} (x - 7) = 1 - lo g_{4} (x - 4)

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

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

(lo g_{3} (x))^{2} = 4 lo g_{3} (x)

lo g_{a} (5) = - 2

What is the answer to log_{5}(x)+log_{x}(25)=3 ?
The answer to log_{5}(x)+log_{x}(25)=3 is x=25,x=5
Solve for x: log_{5}(x)+log_{x}(25)=3
The solution is x=25,x=5