How do you solve #3^(2x) = 5#?

1 Answer
Johnson Z.
Feb 27, 2016

#x~~0.73#

Explanation:

#1#. Notice that the powers on both sides of the equation do not have the same base. Thus, you must log both sides.

#log(3^(2x))=log(5)#

#2#. Recall the log rule: #log_b(m^color(red)(n))=color(red)(n)log_b(m)#. Thus, in your equation, bring down the exponent, #2x#.

#2xlog(3)=log(5)#

#3#. Solve for #x#.

#2x=log(5)/log(3)#

#x=log(5)/(2log(3))#

#color(green)(x~~0.73)#

Related questions
See all questions in Logarithmic Models
Impact of this question
2361 views around the world
You can reuse this answer
Creative Commons License