What is the answer to sqrt(1+log_{2)(x)}+sqrt(4*log_{4)(x)-2}=4 ?

The answer to sqrt(1+log_{2)(x)}+sqrt(4*log_{4)(x)-2}=4 is x=8

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sqrt(1+log_{2)(x)}+sqrt(4*log_{4)(x)-2}=4

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

x = 8

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{4} (x) = u

1 + 2 u + 4 u - 2 = 4

Solve

1 + 2 u + 4 u - 2 = 4 : u = \frac{3}{2}

u = \frac{3}{2}

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = \frac{3}{2} : x = 8

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

lo g_{25} (x) = 3

lo g_{10} (9 x) = \frac{1}{2}

lo g_{4} (x + 9) = 3

lo g_{3} (x) = lo g_{9} (5 x + 6)

lo g_{3} (∣ 2 x - 7 ∣) = 1

What is the answer to sqrt(1+log_{2)(x)}+sqrt(4*log_{4)(x)-2}=4 ?
The answer to sqrt(1+log_{2)(x)}+sqrt(4*log_{4)(x)-2}=4 is x=8
Solve for x: sqrt(1+log_{2)(x)}+sqrt(4*log_{4)(x)-2}=4
The solution is x=8