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

The answer to (log_{10}(x))^2-log_{10}(x^3)+2=0 is x=100,x=10

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

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

x = 100, x = 10

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{10} (x) = u

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

Solve

u^{2} - 3 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 = 10

x = 100, x = 10

Verify Solutions:

x = 100

True

, x = 10

True

The solutions are

x = 100, x = 10

n (x) = 3.5 ln (x + 1)

\frac{lo g _{10} ( 10 - x ^{2} )}{lo g _{10} ( 5 - 2 x )} = 2

3 - lo g_{3} (p) = lo g_{p} (9)

800 = 24 x + ln (\frac{x}{45})

lo g_{2} (x) = 2022

What is the answer to (log_{10}(x))^2-log_{10}(x^3)+2=0 ?
The answer to (log_{10}(x))^2-log_{10}(x^3)+2=0 is x=100,x=10
Solve for x: (log_{10}(x))^2-log_{10}(x^3)+2=0
The solution is x=100,x=10