What is the answer to 6log_{x}(2)+log_{2}(x)-5=0 ?

The answer to 6log_{x}(2)+log_{2}(x)-5=0 is x=8,x=4

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6log_{x}(2)+log_{2}(x)-5=0

6 lo g_{x} (2) + lo g_{2} (x) - 5 = 0

x = 8, x = 4

Solution steps

6 lo g_{x} (2) + lo g_{2} (x) - 5 = 0

Apply log rules

\frac{6}{lo g _{2} ( x )} + lo g_{2} (x) - 5 = 0

Rewrite the equation with

lo g_{2} (x) = u

\frac{6}{u} + u - 5 = 0

Solve

\frac{6}{u} + u - 5 = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

Solve

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

x = 8, x = 4

Verify Solutions:

x = 8

True

, x = 4

True

The solutions are

x = 8, x = 4

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

ln (3) - ln (x^{2} + 2) = 1

2 lo g_{4} (3 x - 1) + 5 = 7

lo g_{7} (5 y + 4) = 2

D = 12 - ln (p)

What is the answer to 6log_{x}(2)+log_{2}(x)-5=0 ?
The answer to 6log_{x}(2)+log_{2}(x)-5=0 is x=8,x=4
Solve for x: 6log_{x}(2)+log_{2}(x)-5=0
The solution is x=8,x=4