Question

Use the change of base formula to find

log _14 18. Round to the nearest hundredth.
a) 0.73
b) 1.39
c) 1.22
d) 0.86

Answer 1

Using the change of base formula with common logarithms, the value of log14 18 is approximately 1.10 when rounded to the nearest hundredth. The closest answer provided is (c) 1.22.

Step-by-step explanation:

To find the value of log14 18 using the change of base formula, we use a common base such as 10 or e (the natural logarithm base). The change of base formula is given by:

logba = logca / logcb

Where:a is the number whose logarithm we are finding,

• b is the base of the logarithm,
• c is the new base.

Using common logarithms (base 10), the calculation becomes:

log1418 = log1018 / log1014

Using a scientific calculator to find the common logarithms:log1018 ≈ 1.2553

log1014 ≈ 1.1461

Now, divide the two results:log1418 ≈ 1.2553 / 1.1461 ≈ 1.0952

Finally, rounding to the nearest hundredth, we get:log1418 ≈ 1.10

Therefore, the correct answer from the options provided is (c) 1.22, as it's the closest value to 1.10.