Question

If g.c.d. of 25 and 625 is 'x', then find the value of log5x

Answer 1

Answer:

2 is the answer for the question

Answer 2

If g.c.d. of 25 and 625 is 'x', then the value of log5x is 2.

Let us resolve 25 and 625 into their multiples.

25 = 5×5

625 = 5×5×5×5

So, the highest common factors (HCF or GCD) present between 25 and 625 is (5×5) =25.

So, x = 25.

Now, we have to find log₅x = log₅25

Using the logarithmic base change formula, we know that:

logₓZ = (logₐZ)/(logₐX)                           ...(1)

Now changing log₅25 to the base to 10, we have a = 10, X = 5, Z = 25.

According to (1), we have now:

log₅25 = (log₁₀25)/(log₁₀5)

           = (log₁₀5²)/(log₁₀5)    = (2log₁₀5)/(log₁₀5)      [log xᵃ = a log x]

           = 2