Questions: Due Saturday, Oct 19, 11:59pm PDT CURRENT OBJECTIVE Working with exponential expressions Question Solve the equation (7^5 x+17=49). Provide your answer below: [ x= ]

Due Saturday, Oct 19, 11:59pm PDT CURRENT OBJECTIVE Working with exponential expressions Question Solve the equation (7^5 x+17=49). Provide your answer below: [ x= ]
Transcript text: Due Saturday, Oct 19, 11:59pm PDT CURRENT OBJECTIVE Working with exponential expressions Question Solve the equation $7^{5 x+17}=49$. Provide your answer below: \[ x= \] $\square$ Content attribution
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Solution

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Solution Steps

To solve the equation \(7^{5x + 17} = 49\), we can use the property of exponents that allows us to express 49 as a power of 7. Since \(49 = 7^2\), we can set the exponents equal to each other and solve for \(x\).

Solution Approach
  1. Rewrite 49 as \(7^2\).
  2. Set the exponents equal to each other: \(5x + 17 = 2\).
  3. Solve the resulting linear equation for \(x\).
Step 1: Rewrite the Equation

We start with the equation: \[ 7^{5x + 17} = 49 \] Recognizing that \(49\) can be expressed as \(7^2\), we rewrite the equation as: \[ 7^{5x + 17} = 7^2 \]

Step 2: Set the Exponents Equal

Since the bases are the same, we can set the exponents equal to each other: \[ 5x + 17 = 2 \]

Step 3: Solve for \(x\)

To isolate \(x\), we first subtract \(17\) from both sides: \[ 5x = 2 - 17 \] \[ 5x = -15 \] Next, we divide both sides by \(5\): \[ x = -3 \]

Final Answer

\[ \boxed{x = -3} \]

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