How do you evaluate #log_49 343#?

2 Answers
May 25, 2018

#log_49 343 = 3/2#

Explanation:

#log_49 343#
#=log_7(343)/log_7(49)#
#=log_7(7^3)/log_7(7^2)#
#=(3log_7(7))/(2log_7(7))#
#=3/2#

Alternatively, you could say #343 = 49 ^ (3/2)#

The answer will follow immediately.

May 26, 2018

#log_(49)343=3/2#

Explanation:

#x=log_(49)343#

#=>49^x=343#

#=>(7^2)^x=343#

#7^(2x)=343#

but #7^3=343#

#:.2x=3#

#=>x=3/2#

#log_(49)343=3/2#