If log 3 base a=2 and log 8 base b=3,then logged b base a is?

1 Answer
May 16, 2018

If #log_a3=2 and log_b8=3# then what is #log_ab#?
#a=sqrt(3)# & #b=2# so using a calculator #log_sqrt(3)2=1.262# (4.S.F)

Explanation:

#log_a3=2# (now raise both sides as a power of a)
-> # a^(log_a3)= a^2# (now use exponent of log rule; raising the logarithm of a number as a power of its base gives the number.)
-> #3=a^2# (now take the principal root)
-> #a=sqrt(3)#

Similarly,
#log_b8=3#
-> #8=b^3#
-> #b=2#

Finally,
input #log_sqrt(3)2# into your calculator giving #1.262# (4.S.F)

You can also rewrite the answer using the change of base formula:
# log_yx =log_zx/log_zy#
in our case
# log_sqrt(3)2 =(log_3 2)/log_3sqrt(3)#
-> = #2log_3 2#
Thanks ciumes :)