How do you solve the equation #2log_3 sqrt(x) = log_3 (6x - 1)#?

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Answer 1 · 2017-03-25T01:57:46

#{1/5}#

Use the following laws of logarithms to solve this problem:

#alogn = logn^a#
#logn = logm -> n = m#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We have:

#log_3 (sqrt(x))^2 =log_3(6x - 1)#

#log_3 x = log_3(6x - 1)#

#x = 6x - 1#

#1 = 5x#

#x = 1/5#

If you check in the equation, you will find this solution indeed works.

Hopefully this helps!