What is the answer to log_{10}(x^4-4)-log_{10}(x^2+2)=0 ?

The answer to log_{10}(x^4-4)-log_{10}(x^2+2)=0 is x=sqrt(3),x=-sqrt(3)

Solve for x: log_{10}(x^4-4)-log_{10}(x^2+2)=0

The solution is x=sqrt(3),x=-sqrt(3)

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lo g_{10} (x^{4} - 4) - lo g_{10} (x^{2} + 2) = 0

x = 3, x = - 3

Decimal

x = 1.73205 \dots, x = - 1.73205 \dots

Solution steps

lo g_{10} (x^{4} - 4) - lo g_{10} (x^{2} + 2) = 0

Add

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

to both sides

lo g_{10} (x^{4} - 4) - lo g_{10} (x^{2} + 2) + lo g_{10} (x^{2} + 2) = 0 + lo g_{10} (x^{2} + 2)

Simplify

lo g_{10} (x^{4} - 4) = lo g_{10} (x^{2} + 2)

Apply log rules

x^{4} - 4 = x^{2} + 2

Solve

x^{4} - 4 = x^{2} + 2 : x = 3, x = - 3

x = 3, x = - 3

Verify Solutions:

x = 3

True

, x = - 3

True

The solutions are

x = 3, x = - 3

2 lo g_{7} (x - 1) = 0

x, 5 x + 3 ln (x - 4) = 25

10 lo g_{10} (\frac{x}{20}) = 5

lo g_{a} (16) = \frac{1}{2}

lo g_{3} (5) + lo g_{3} (x - 4) = 2

What is the answer to log_{10}(x^4-4)-log_{10}(x^2+2)=0 ?
The answer to log_{10}(x^4-4)-log_{10}(x^2+2)=0 is x=sqrt(3),x=-sqrt(3)
Solve for x: log_{10}(x^4-4)-log_{10}(x^2+2)=0
The solution is x=sqrt(3),x=-sqrt(3)