Question

Show that solving the equation 3^2x=4 by taking common logarithms of both sides is equivalent to solving it by taking logarithms of base 3 of both sides.

Answer 1

Explanation:

Case I: use common logs:

2x log 3 = log 4, or 2x(0.47712) = 0.60206

Solving for x, we get 0.95424x = 0.60206, and then x = 0.60206/0.95424.

x is then x = 0.631

Case II: use logs to the base 3:

2x (log to the base 3 of 3) = (log to the base 3 of 4)

This simplifies to 2x(1) = 2x = (log 4)/log 3 = 1.262. Finally, we divide this

result by 2, obtaining x = 0.631