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

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

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

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

x = 5

Solution steps

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

Apply log rules

lo g_{5} (x) + \frac{1}{lo g _{5} ( x )} = 2

Rewrite the equation with

lo g_{5} (x) = u

u + \frac{1}{u} = 2

Solve

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

u = 1

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{3} (\frac{2 x - 3}{4}) = lo g_{3} (x + 1)

lo g_{10} (x + 2) - lo g_{10} (x + 1) = 1

lo g_{10} (5 x + 2) = 3

ln (x + 3) + ln (x - 1) - 3 = 0

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

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