Question

1. estimate the logarithmic $\log_{3} 220$ to the nearest tenth.

type a response

1. estimate the logarithmic to the nearest tenth. $\log_{4} 40$

type a response

Explanation:

Step1: Apply change of base formula

$\log_{3}220 = \frac{\ln 220}{\ln 3}$

Step2: Calculate natural logs

$\ln 220 \approx 5.3936$, $\ln 3 \approx 1.0986$

Step3: Divide to find value

$\frac{5.3936}{1.0986} \approx 4.9$
---

Step1: Apply change of base formula

$\log_{4}40 = \frac{\ln 40}{\ln 4}$

Step2: Calculate natural logs

$\ln 40 \approx 3.6889$, $\ln 4 \approx 1.3863$

Step3: Divide to find value

$\frac{3.6889}{1.3863} \approx 2.7$

Answer:

1. $4.9$
2. $2.7$