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

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

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(log_{10}(x))^2+2log_{10}(x)=3

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

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

Decimal

x = 10, x = 0.001

Solution steps

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

Rewrite the equation with

lo g_{10} (x) = u

(u)^{2} + 2 u = 3

Solve

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

u = 1, u = - 3

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 1 : x = 10

Solve

lo g_{10} (x) = - 3 : x = \frac{1}{1000}

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

Verify Solutions:

x = 10

True

, x = \frac{1}{1000}

True

The solutions are

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

lo g_{10} (x) + lo g_{10} (x + 5) = 1

lo g_{10} (x) + lo g_{10} (x + 5) = 6

lo g_{3} (x) = 8

y, - y = lo g_{10} (x)

lo g_{10} (x) = 2

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