Question

module 6: mastery
mi algebra ii - s1 / module 6 / lesson 90

1. using a calculator, evaluate the logarithmic or natural logarithmic expressions on the left and match them to their values on the

a. ≈0.297
b. ≈0.774
c. ≈0.443
d. ≈0.2339

1. \\(\frac{\log 9}{4}\\)
2. \\(\frac{\ln 8}{7}\\)
3. \\(\frac{\log 4}{\log 6}\\)
4. \\(\frac{\ln 7}{2\ln 9}\\)

Explanation:

Step1: Evaluate $\frac{\log 9}{4}$

Using a calculator, $\log 9\approx0.9542$, then $\frac{0.9542}{4}\approx0.239$.

Step2: Evaluate $\frac{\ln 8}{7}$

$\ln 8\approx2.0794$, so $\frac{2.0794}{7}\approx0.297$.

Step3: Evaluate $\frac{\log 4}{\log 6}$

$\log 4\approx0.6021$, $\log 6\approx0.7782$, then $\frac{0.6021}{0.7782}\approx0.774$.

Step4: Evaluate $\frac{\ln 7}{2\ln 9}$

$\ln 7\approx1.9459$, $\ln 9\approx2.1972$, $2\ln 9\approx4.3944$, so $\frac{1.9459}{4.3944}\approx0.443$.

Answer:

1. $\frac{\log 9}{4}\approx0.239$ (matches d)
2. $\frac{\ln 8}{7}\approx0.297$ (matches a)
3. $\frac{\log 4}{\log 6}\approx0.774$ (matches b)
4. $\frac{\ln 7}{2\ln 9}\approx0.443$ (matches c)