How do you find the value of #log_7 4# using the change of base formula?

1 Answer
Nov 1, 2016

Answer:

#0.715#

Explanation:

You can use the change of base formula to be able to use #log_10#

#log_7 4 = (log_10 4)/(log_10 7)#

This is now calculated with a calculator:

#=0.715#

The follow explains where the rule comes from...

#log_7 4 = x " "hArr" " 7^x = 4" larr# log both sides

#color(white)(xxxxxxxxxxxxxx)log7^x = log 4" "larr# power law

#color(white)(xxxxxxxxxx.xxx)xlog7 = log 4" "larr# isolate x

#color(white)(xxxxxxxxxxxxxxxxx)x = log4/log7#