How do you solve #8^(2n)>52^(4n+3)#?

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Answer 1 · 2016-11-06T03:42:19

Take the natural logarithm of both sides.

#ln(8^(2n)) > ln(52^(4n + 3))#

Use the rule #loga^n = nloga# to simplify further.

#(2n)ln8 > (4n + 3)ln52#

#2nln8 > 4nln52 + 3ln52#

#-3ln52 > 4nln52 - 2nln8#

#-3ln52> 2n(2ln52 - ln8)#

#(-3ln52)/(2ln52 - ln8) > 2n#

#-1.0178 > n#

Hopefully this helps!