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

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

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

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

a = 16

Solution steps

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

f (x) = g (x),

then

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

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

Simplify

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

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

Solve

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

a = 16

Verify Solutions:

a = 16

True

The solution is

a = 16

0.678 = ln (x^{3})

lo g_{7} (25) = 2 lo g_{7} (x)

lo g_{2} (x) = - 1.5

\frac{ln ( 2 b )}{ln ( 4 b )} = 4

0.5 = ln (x)

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