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

The answer to (log_{10}(x))^2-log_{10}(x)-2=0 is x=100,x= 1/10

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

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

x = 100, x = \frac{1}{10}

Decimal

x = 100, x = 0.1

Solution steps

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

Rewrite the equation with

lo g_{10} (x) = u

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

Solve

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

u = 2, u = - 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 2 : x = 100

Solve

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

x = 100, x = \frac{1}{10}

Verify Solutions:

x = 100

True

, x = \frac{1}{10}

True

The solutions are

x = 100, x = \frac{1}{10}

lo g_{2} (x - 1) = - 2022

(lo g_{2} (x))^{2} - 5 \cdot lo g_{2} (x) + 6 = 0

lo g_{10} (a) = 6

2 lo g_{10} (3 x) + lo g_{10} (18 x) = 27

lo g_{6} (x) + lo g_{6} (x + 5) = 2

What is the answer to (log_{10}(x))^2-log_{10}(x)-2=0 ?
The answer to (log_{10}(x))^2-log_{10}(x)-2=0 is x=100,x= 1/10
Solve for x: (log_{10}(x))^2-log_{10}(x)-2=0
The solution is x=100,x= 1/10