2x = 1000

The Equation

Prove the equation:

2^x = 1000

If f(x) = g(x), then, 1n (f(x)) = 1n (g(x))

1n (2^x) = 1n (1000)

Applying rule of log: log_a(x^b) = b · log_a(x)

1n (2^x) = x1n(2)

x1n (2) = 1n (1000)

Solve x1n (2) = 1n (1000) :  x= 31n(10)/1n (2)

x1n (2) = 1n (1000)

x1n(2)/1n (2) = 1n (1000)/ 1n (2)

x= 31n (10)/1n (2)

Therefor the value of x= 31n(10)/ 1n(2).

Hence in the equation 2^x = 1000; the decimal value of x= 9.96578.