Solve \((\log (x))^{2}-3\log (x)=\log \left(x^{2}\rig

Question

Solve the equation

x_{1} = 10, x_{2} = 10000

Evaluate

(lo g_{10} (x))^{2} - 3 lo g_{10} (x) = lo g_{10} (x^{2}) - 4

Find the domain

More Steps

(lo g_{10} (x))^{2} - 3 lo g_{10} (x) = lo g_{10} (x^{2}) - 4, x > 0

Move the expression to the left side

(lo g_{10} (x))^{2} - 3 lo g_{10} (x) - (lo g_{10} (x^{2}) - 4) = 0

Subtract the terms

More Steps

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

Use lo g_{a} b^{n} = n lo g_{a} b to simplify the expression

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

Factor the expression

(lo g_{10} (x) - 4) (lo g_{10} (x) - 1) = 0

Separate the equation into 2 possible cases

lo g_{10} (x) - 4 = 0 lo g_{10} (x) - 1 = 0

Solve the equation

More Steps

x = 10000 lo g_{10} (x) - 1 = 0

Solve the equation

More Steps

x = 10000 x = 10

Check if the solution is in the defined range

x = 10000 x = 10, x > 0

Find the intersection of the solution and the defined range

x = 10000 x = 10

Solution

x_{1} = 10, x_{2} = 10000

Show Solution