Final answer:
To approximate log3 48, express 48 as a power of 3 and use the property of logarithms to find that log3 48 ≈ 1.44.
Step-by-step explanation:
To find the approximate value of log3 48, we use the given values that 48 ≈ 1.683 and log3 ≈ .48. We can write 48 as a power of 3 using the approximation to express 48 in terms of exponentials.
The logarithm log3 48 can then be calculated using the property that the logarithm of a power, logb (an), is n multiplied by the logarithm of the base, logb a. First express 48 as a power of 3: 48 ≈ 1.683
Now we calculate the logarithm of 48 to the base 3:
log3 48 ≈ log3 1.683
Apply the property of logarithms:
log3 48 ≈ 3 × log3 1.68
Since log3 ≈ .48, we can substitute:
log3 48 ≈ 3 × .48
Finally, calculate the approximate value:
log3 48 ≈ 1.44