Question

find the value of x ​

Answer 1

Answer:

3.7210

Step-by-step explanation:

Take logs (base 10) of both sides:

5ˣ = 400

=>  log 5ˣ = log 400

=>  x log 5 = log 400      ... (*)

Let's work out log 5 and log 400 separately.

log 5 = log ( 10 / 2 ) =  log 10 - log 2

        = 1 - 0.3010 = 0.6990  ( using the given value for log 2 ).

log 400 = log ( 4 × 100 ) = log 4 + log 100 = log 2² + log 100

            = 2 log 2 + log 100 = 0.6010 + 2 = 2.6010  ( using the given value for log 2 ).

Going back to equation (*), we now have

x = log 400 / log 5 = 2.6010 / 0.6990 = 3.7210