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

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

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

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

x = 4

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

u = 4 - \frac{4}{u}

Solve

u = 4 - \frac{4}{u} : u = 2

u = 2

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

lo g_{x} (6 x - 8) = 2

ln (x + 3) = 4

ln (x) = 8

lo g_{3} (2 x - 1) = 2

lo g_{2} (x) = 4.5

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