The ㏒ of 64 to the base 2√2 is
Answers
Step-by-step explanation:
please answer my two physics questions
Answer:
Answer: 4.00044
Calculation:
To evaluate the logarithm of 64 to the base 2(2)½, we need to recall the formula to transform logarithm from a known base a to another base b. The formula is:
log N to the base b = (1/logₐb) x logₐN
where N is any number whose logarithm to base b is required. Since N and b are given, logₐN and logₐb are known from the Tables, and from these, log N to base b can be computed.
In the present problem, N = 64 and b = 2√ 2 = 2^3/2 . We take a = 10 since logarithms of all numbers to base 10 are known and tabulated. Thus,
log 64 to the base 2^3/2 = 1/[log₁₀ (2^3/2)] x log₁₀ 64
=[1/(3/2 x log₁₀ 2)] x 1.8062 = [2/(3 x log₁₀ 2)] x 1.8062 = (2 x 1.8062)/(3x0.3010)
=3.6124/.9030
= 4.00044 (Answer).