Question

Solve the equation for x, accurate to three decimal places: 2^x = 50.

Answer 1

The exponential equation is 2^x = 50

if n and a are positive real numbers, and a is not equal to 1, then

a^x = n, then log _a n = x

2^x = 50, then log ₂ 50 = x

Solution x = 5.643

(0r)

The exponential equation is 2^x = 50

Take common log on each side.

log(2^x) = log(50)

Power rule: log_bA^C = C(log_bA)

x log (2) = log(50)

x = log(50)/log(2)

x = 1.6989/0.3010

x = 5.643

Solution x  = 5.643.