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Solve the expressionlog2 (5x-4)=4

User Eightball
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Recall the following property of logarithms:


\log _a(b)=c\Leftrightarrow b=a^c

Then:


\begin{gathered} \log _2(5x-4)=4 \\ \Leftrightarrow \\ 5x-4=2^4 \end{gathered}

Solve for x in the new equation:


\begin{gathered} 5x-4=2^4 \\ \Rightarrow5x-4=16 \\ \Rightarrow5x=16+4 \\ \Rightarrow5x=20 \\ \Rightarrow x=(20)/(5) \\ \Rightarrow x=4 \end{gathered}

Replace x=4 into the original expression to confirm the result:


\begin{gathered} \log _2(5x-4)=\log _2(5(4)-4) \\ =\log _2(20-4) \\ =\log _2(16) \\ =4 \end{gathered}

Therefore, the answer is: x=4

User Clorichel
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