Questions: 4^(2x-5) = 2^(3x+7)

4^(2x-5) = 2^(3x+7)
Transcript text: $4^{2 x-5}=2^{3 x+7}$
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Solution

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Solution Steps

Step 1: Rewrite the Equation

We start with the equation \(4^{2x-5} = 2^{3x+7}\). Since \(4\) can be expressed as \(2^2\), we rewrite the left side of the equation: \[ (2^2)^{2x-5} = 2^{3x+7} \]

Step 2: Simplify the Exponents

Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we simplify the left side: \[ 2^{4x - 10} = 2^{3x + 7} \]

Step 3: Set the Exponents Equal

Since the bases are the same, we can set the exponents equal to each other: \[ 4x - 10 = 3x + 7 \]

Step 4: Solve for \(x\)

To isolate \(x\), we rearrange the equation: \[ 4x - 3x = 7 + 10 \] This simplifies to: \[ x = 17 \]

Final Answer

\(\boxed{x = 17}\)

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-5/3^2= (-5/3)^3=