What is the answer to log_{4}(x)+log_{x}(4)=2 ?

The answer to log_{4}(x)+log_{x}(4)=2 is x=4

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log_{4}(x)+log_{x}(4)=2

lo g_{4} (x) + lo g_{x} (4) = 2

x = 4

Solution steps

lo g_{4} (x) + lo g_{x} (4) = 2

Apply log rules

lo g_{4} (x) + \frac{1}{lo g _{4} ( x )} = 2

Rewrite the equation with

lo g_{4} (x) = u

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

Solve

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

u = 1

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 1 : x = 4

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

lo g_{5} (b) = 3

lo g_{5} (x) = 0

y ln (y + 2) = 0

ln (x - 3) + ln (3) = ln (18)

lo g_{2} (x) + 5 lo g_{4} (x) = 14

What is the answer to log_{4}(x)+log_{x}(4)=2 ?
The answer to log_{4}(x)+log_{x}(4)=2 is x=4
Solve for x: log_{4}(x)+log_{x}(4)=2
The solution is x=4