What is the answer to (log_{10}(x))^2-log_{10}(x^2)-3=0 ?

The answer to (log_{10}(x))^2-log_{10}(x^2)-3=0 is x=1000,x= 1/10

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(log_{10}(x))^2-log_{10}(x^2)-3=0

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

x = 1000, x = \frac{1}{10}

Decimal

x = 1000, x = 0.1

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{10} (x) = u

(u)^{2} - 2 u - 3 = 0

Solve

u^{2} - 2 u - 3 = 0 : u = 3, u = - 1

u = 3, u = - 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 3 : x = 1000

Solve

lo g_{10} (x) = - 1 : x = \frac{1}{10}

x = 1000, x = \frac{1}{10}

Verify Solutions:

x = 1000

True

, x = \frac{1}{10}

True

The solutions are

x = 1000, x = \frac{1}{10}

a, lo g_{3} (a) + 1 = 2 lo g_{10} (b)

lo g_{2} (3 - x) = lo g_{4} (2 x^{18})

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

ln (x) + 5 = 10

lo g_{3} (x + 1) - lo g_{3} (27) = 4

What is the answer to (log_{10}(x))^2-log_{10}(x^2)-3=0 ?
The answer to (log_{10}(x))^2-log_{10}(x^2)-3=0 is x=1000,x= 1/10
Solve for x: (log_{10}(x))^2-log_{10}(x^2)-3=0
The solution is x=1000,x= 1/10