Question

Si log2 = a
Hallar log25
a) 2(a-1)
b) 2(a+1)
c) 2(2+a)
d) 2(1-a)

Answer 1

Given that log2 equals a, the value of log2(5) is calculated using the properties of logarithms. Since 5 can be written as 2^2 × 2^-1, by applying the property of logarithms and the given value a, the answer is simply a.

Step-by-step explanation:

To find the value of log2(5) when log2 is given to be a, we can use the property of logarithms that expresses the logarithm of a number as the difference between the logarithms of its factors. Specifically, we can write 5 as 22 × 2-1, and use the known value of a to find the answer:

• log2(5) = log2(22 × 2-1)
• log2(5) = log2(22) + log2(2-1) (using the property logb(mn) = logb(m) + logb(n))
• log2(5) = 2 × log2(2) - log2(2) (because log base b of b is 1)
• log2(5) = 2 × a - a
• log2(5) = a (since 2a - a = a)

Thus, the value of log2(5) using the given information is simply a.