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

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

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

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

x = 2

Solution steps

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

Rewrite the equation with

2^{4 x} = u

lo g_{4} (u) = 2^{l o g_{2} (4)}

Solve

lo g_{4} (u) = 2^{l o g_{2} (4)} : u = 256

u = 256

Substitute back

u = 2^{4 x},

solve for

x

Solve

2^{4 x} = 256 : x = 2

x = 2

5^{2 x - 1} = 2^{x + 1}

5^{x} + 2 = 625

(\frac{1}{4})^{2 x - 2} = 256

1 6^{x} + 2 0^{x} = 2 0^{x}

(2^{2})^{m} - (2^{2})^{n} = 240

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