Solve log5(x^22x)=log5(x^210)

Evaluate

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

Remove the parentheses

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

Multiply

More Steps

2 lo g_{10} (5) \times x^{3} = lo g_{10} (5) \times x^{2} \times 10

Use the commutative property to reorder the terms

2 lo g_{10} (5) \times x^{3} = 10 lo g_{10} (5) \times x^{2}

Add or subtract both sides

2 lo g_{10} (5) \times x^{3} - 10 lo g_{10} (5) \times x^{2} = 0

Factor the expression

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

Divide both sides

x^{2} (x - 5) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x - 5 = 0

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

x = 0 x - 5 = 0

Solve the equation

More Steps

x = 0 x = 5

Solution

x_{1} = 0, x_{2} = 5

Solve the equation