How do you solve log_3 32 = x?

1 Answer
Nov 27, 2015

This is already 'solved' in that x = log_3 32

but you can use the change of base formula to find:

x = log(32)/log(3) = ln(32)/ln(3) ~~ 3.15465

Explanation:

The change of base formula tells use that if a, b, c > 0 then:

log_a b = (log_c b)/(log_c a)

This allows us to express log_3 32 in terms of common (base 10) logarithms or natural (base e) logarithms:

log_3 32 = log(32)/log(3) = ln(32)/ln(3) ~~ 3.15465