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

The answer to log_{4}(x^2)+log_{4}(2)=4 is x=8sqrt(2),x=-8sqrt(2)

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

The solution is x=8sqrt(2),x=-8sqrt(2)

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

x = 82, x = - 82

Decimal Notation

x = 11.31370 \dots, x = - 11.31370 \dots

Solution steps

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

Move

lo g_{4} (2)

to the right side

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

Apply log rules

x^{2} = 4^{4 - \frac{1}{2}}

Solve

x^{2} = 4^{4 - \frac{1}{2}} : x = 82, x = - 82

x = 82, x = - 82

Verify Solutions:

x = 82

True

, x = - 82

True

The solutions are

x = 82, x = - 82

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

9 = - lo g_{10} (x)

lo g_{8} (2 (x^{3} + 5)) = 2

lo g_{8} (x) = - \frac{1}{3}

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

What is the answer to log_{4}(x^2)+log_{4}(2)=4 ?
The answer to log_{4}(x^2)+log_{4}(2)=4 is x=8sqrt(2),x=-8sqrt(2)
Solve for x: log_{4}(x^2)+log_{4}(2)=4
The solution is x=8sqrt(2),x=-8sqrt(2)