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

The answer to log_{4}(x^4)=4 is x=4,x=-4

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log_{4}(x^4)=4

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

x = 4, x = - 4

Solution steps

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

Apply exponent rule:

a^{2 \cdot n} = (a^{2})^{n}

x^{4} = (x^{2})^{2}

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

Apply log rules

x^{2} = 16

Solve

x^{2} = 16 : x = 4, x = - 4

x = 4, x = - 4

Verify Solutions:

x = 4

True

, x = - 4

True

The solutions are

x = 4, x = - 4

lo g_{10} (x^{2} + 16) = 2

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

x, ln (x + y - 2) = 1

lo g_{2} (lo g_{3} (2 x - 1)) = 2

y, x = ln (y + 1)