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

The answer to log_{2}(4^x)=-2 is x=-1

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

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

x = - 1

Solution steps

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

Rewrite the equation with

4^{x} = u

lo g_{2} (u) = - 2

Solve

lo g_{2} (u) = - 2 : u = \frac{1}{4}

u = \frac{1}{4}

Substitute back

u = 4^{x},

solve for

x

Solve

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

x = - 1

(\frac{1}{4})^{x - 1} = 1 6^{x + 2}

0 = x^{2} e^{- x^{2}}

2^{x} = 41

73 = 2 5^{x}

2^{x} = 80