Solve 5(x^4)=log5(x^22)

Evaluate

5 x^{4} = lo g_{10} (5) \times (x^{2} \times 2)

Remove the parentheses

5 x^{4} = lo g_{10} (5) \times x^{2} \times 2

Use the commutative property to reorder the terms

5 x^{4} = 2 lo g_{10} (5) \times x^{2}

Add or subtract both sides

5 x^{4} - 2 lo g_{10} (5) \times x^{2} = 0

Factor the expression

x^{2} (5 x^{2} - 2 lo g_{10} (5)) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5 x^{2} - 2 lo g_{10} (5) = 0

The only way a power can be 0 is when the base equals 0

x = 0 5 x^{2} - 2 lo g_{10} (5) = 0

Solve the equation

More Steps

x = 0 x = \frac{10 lo g _{10} ( 5 )}{5} x = - \frac{10 lo g _{10} ( 5 )}{5}

Solution

x_{1} = - \frac{10 lo g _{10} ( 5 )}{5}, x_{2} = 0, x_{3} = \frac{10 lo g _{10} ( 5 )}{5}

Alternative Form

x_{1} \approx - 0.528761, x_{2} = 0, x_{3} \approx 0.528761

Solve the equation