college algebra

Question

use common logarithms or natural logarithms and a calculator to evaluate to four decimal places

 

log₂₀³⁸⁴ =

Answer 1

log ₂₀384

 

here we can use change of base formula

Change of base formula. Log_b x = Log x/Log b.

Pick a new base and the formula says it is equal to the log of the number in the new base divided by the log of the old base in the new base.  Change to base 10 and use your calculator.

 

log₂₀384 = (log 384)/(log 20) = 1.9864

Answer 2

Change of base:  lob_a b = (log b)/(log a)

 

log₂₀384 = (log 384)/(log 20) = 1.9864