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Help solving e 27 log2(4)^3e=864(1/16)

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1 vote

Answer:

e = 1/3

Step-by-step explanation:

The initial expression is:


27\log _24^(3e)=864((1)/(16))

First, let's divide 864 by 16 to get:


\begin{gathered} 27\log _24^(3e)=(864)/(16) \\ 27\log _24^(3e)=54 \end{gathered}

Now, divide both sides by 27


\begin{gathered} (27\log _24^(3e))/(27)=(54)/(27) \\ \log _24^(3e)=2 \end{gathered}

Then, by properties of the logarithms, the exponent of the 4 can multiply the expression as:


3e\log _24=2

Since log₂4 = 2, we get:


\begin{gathered} 3e(2)=2 \\ 6e=2 \\ (6e)/(6)=(2)/(6) \\ e=(1)/(3) \end{gathered}

Therefore, the value of e is 1/3

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