What is the answer to log_{2}(x)+log_{x}(4)=3 ?

The answer to log_{2}(x)+log_{x}(4)=3 is x=4,x=2

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log_{2}(x)+log_{x}(4)=3

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

x = 4, x = 2

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (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_{2} (x),

solve for

x

Solve

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

Solve

lo g_{2} (x) = 1 : x = 2

x = 4, x = 2

Verify Solutions:

x = 4

True

, x = 2

True

The solutions are

x = 4, x = 2

7 - 2 ln (x) = 2

H, p = - lo g_{10} (H)

10 lo g_{10} (x) = 3

10 lo g_{10} (x) = 1

2 = lo g_{10} (4 π x) - lo g_{10} (π)

What is the answer to log_{2}(x)+log_{x}(4)=3 ?
The answer to log_{2}(x)+log_{x}(4)=3 is x=4,x=2
Solve for x: log_{2}(x)+log_{x}(4)=3
The solution is x=4,x=2