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!

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