Use a calculator and the change-of-base formula to find the logarithm. Round your answe decimal places. \( \log _{7} 4=\square \)

To find \( \log_{7} 4 \) using the change-of-base formula, you convert it to a fraction of logarithms with a convenient base. The change-of-base formula states that \( \log_{b} a = \frac{\log_{c} a}{\log_{c} b} \). Here, we can use base 10 or base \( e \). Let’s use base 10: \[ \log_{7} 4 = \frac{\log_{10} 4}{\log_{10} 7} \approx \frac{0.6021}{0.8451} \approx 0.711 \] So, \( \log_{7} 4 \approx 0.711 \) when rounded to three decimal places. When performing logarithmic calculations, it's easy to mistakenly input the numbers into your calculator the wrong way around. Double-check which number is the base and which is the argument to avoid this common pitfall. Remember that logs can be tricky, but with practice, you’ll navigate them like a pro! Don't forget to check your calculator's settings to ensure you're using the proper log function!