Change of Base Formula
logb x = loga x/loga b
to evaluate log14 41.
(Round your answer to three decimal places.)
i need a step by step preview please
just use the formula
let a = 10, so we can use your standard base 10 logs on your calculator
log14 41 = log 41/log 14 = appr 1.407158..
= 1.407 correct to 3 decimals
check by evaluating 14^1.407 on your calculator.
What did you get?
Step 1: Determine the base for the logarithm you are trying to evaluate, which is 14 in this case.
Step 2: Determine the base for the logarithm you want to convert to, which is 10 (common logarithm) in this case.
Step 3: Apply the change of base formula: logb x = loga x / loga b
In this case, we want to evaluate log14 41, so x = 41, b = 14, and we are converting to base 10.
Using the change of base formula, we have:
log14 41 = log10 41 / log10 14
Step 4: Calculate the values of log10 41 and log10 14 using a calculator.
log10 41 ≈ 1.612
log10 14 ≈ 1.146
Step 5: Substitute the calculated values into the change of base formula:
log14 41 ≈ 1.612 / 1.146
Step 6: Perform the division to find the approximate value of log14 41:
log14 41 ≈ 1.408 (rounded to three decimal places)
Therefore, log14 41 is approximately equal to 1.408 when rounded to three decimal places.
To use the change of base formula to evaluate log14 41, follow these step-by-step instructions:
1. Identify the base of the given logarithm (log14 41). In this case, the base is 14.
2. Identify the desired base to change to. Let's use the common logarithm, which has a base of 10. This means we want to use the change of base formula to rewrite log14 41 as log10 41.
3. Use the change of base formula: logb x = loga x / loga b. In this case, our equation becomes: log14 41 = log10 41 / log10 14.
4. Evaluate the logarithms on the right side of the equation using a calculator. In this case, calculate log10 41 and log10 14.
- Using a calculator, log10 41 ≈ 1.612.
- Similarly, log10 14 ≈ 1.146.
5. Substitute the values back into the change of base formula: log14 41 ≈ 1.612 / 1.146.
6. Calculate the division: log14 41 ≈ 1.407 (rounded to three decimal places).
Therefore, log14 41 is approximately 1.407 when rounded to three decimal places.