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a) \( 4.25^{x+3}=4 \)

Ask by Grant Zimmerman. in South Africa
Jan 20,2025

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\( x = 2\log_{\frac{17}{4}}{(2)} - 3 \)

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Bonus Knowledge

To solve the equation \( 4.25^{x+3}=4 \), let's start by rewriting 4 as a power of 4. Since \( 4 = 4^{1} \), we can express both sides with the same base. This gives us \( 4.25^{x+3} = 4^{1} \). Next, take the logarithm of both sides to isolate \( x \): \[ (x+3) \cdot \log(4.25) = \log(4) \] Now, solve for \( x+3 \): \[ x+3 = \frac{\log(4)}{\log(4.25)} \] Finally, isolate \( x \): \[ x = \frac{\log(4)}{\log(4.25)} - 3 \] When you plug the values into a calculator, you'll find \( x \) to be approximately -2.16. Happy calculating!

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