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

The answer to log_{2}(x)+3log_{x}(2)=4 is x=8,x=2

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

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

x = 8, x = 2

Solution steps

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

Apply log rules

lo g_{2} (x) + \frac{3}{lo g _{2} ( x )} = 4

Rewrite the equation with

lo g_{2} (x) = u

u + \frac{3}{u} = 4

Solve

u + \frac{3}{u} = 4 : u = 3, u = 1

u = 3, u = 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 3 : x = 8

Solve

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

x = 8, x = 2

Verify Solutions:

x = 8

True

, x = 2

True

The solutions are

x = 8, x = 2

2 lo g_{10} (x) ln (10) = ln (4)

lo g_{3} (x^{2} - 8 x) = 2

lo g_{10} (x + 4) = lo g_{10} (2 x - 1)

ln ((x - 2)^{2}) - ln (x) = 0

3 = lo g_{10} (x)

What is the answer to log_{2}(x)+3log_{x}(2)=4 ?
The answer to log_{2}(x)+3log_{x}(2)=4 is x=8,x=2
Solve for x: log_{2}(x)+3log_{x}(2)=4
The solution is x=8,x=2