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

The answer to log_{x}(2^x)= x/4 is x=16

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

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

x = 16

Solution steps

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

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

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

Simplify

x^{l o g_{x} (2^{x})} : 2^{x}

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

Solve

2^{x} = x^{\frac{x}{4}} : x = 16

x = 16

Verify Solutions:

x = 16

True

The solution is

x = 16

ln (a) = ln (3 e^{2}) - 2

lo g_{6} (x - 5) + lo g_{6} (x) = 2

lo g_{6} (x - 1) + lo g_{6} (x) = 1

a = - lo g_{10} (x)

\frac{1}{2} ln (x + 3) - ln (x) = 0

What is the answer to log_{x}(2^x)= x/4 ?
The answer to log_{x}(2^x)= x/4 is x=16
Solve for x: log_{x}(2^x)= x/4
The solution is x=16