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(2) \( 3 \cdot 5^{x}+5^{x+1}=40 \)

Ask by Schneider Thornton. in South Africa
Jan 20,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

\( x = 1 \)

Solution

Solve the equation \( 3*5^x+5^(x+1)=40 \). Solve the equation by following steps: - step0: Solve for \(x\): \(3\times 5^{x}+5^{x+1}=40\) - step1: Add the terms: \(8\times 5^{x}=40\) - step2: Divide both sides: \(\frac{8\times 5^{x}}{8}=\frac{40}{8}\) - step3: Divide the numbers: \(5^{x}=5\) - step4: Set the exponents equal: \(x=1\) The solution to the equation \(3 \cdot 5^{x} + 5^{x+1} = 40\) is \(x = 1\).

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Beyond the Answer

To solve the equation \( 3 \cdot 5^{x} + 5^{x+1} = 40 \), first notice that \( 5^{x+1} = 5 \cdot 5^{x} \). You can rewrite the equation as \( 3 \cdot 5^{x} + 5 \cdot 5^{x} = 40 \). This simplifies to \( (3 + 5) \cdot 5^{x} = 40 \), or \( 8 \cdot 5^{x} = 40 \). Dividing both sides by 8 gives \( 5^{x} = 5 \), which implies \( x = 1 \). If you want to check your solution, substitute \( x = 1 \) back into the original equation: \[ 3 \cdot 5^{1} + 5^{2} = 3 \cdot 5 + 25 = 15 + 25 = 40. \] The equation holds true, confirming that \( x = 1 \) is indeed the correct solution! Happy solving!

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