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

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

Popular >

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

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

x = 100, x = 1

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{10} (x) = u

(u)^{2} = 2 u

Solve

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

u = 2, u = 0

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

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

Solve

lo g_{10} (x) = 0 : x = 1

x = 100, x = 1

Verify Solutions:

x = 100

True

, x = 1

True

The solutions are

x = 100, x = 1

2 lo g_{10} (x) - lo g_{10} (x + 6) = 0

ln (\frac{1}{x}) + ln (2 x^{3}) = ln^{3} (x)

2 lo g_{10} (x) + 1 = lo g_{250} (x)

lo g_{10} (x) - 4 (\frac{1 - x}{2}) = 1

ln (2 x + 1) - ln (x - 6) = 0

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