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

Nov 6, 2016

Take the natural logarithm of both sides.

$\ln \left({8}^{2 n}\right) > \ln \left({52}^{4 n + 3}\right)$

Use the rule $\log {a}^{n} = n \log a$ to simplify further.

$\left(2 n\right) \ln 8 > \left(4 n + 3\right) \ln 52$

$2 n \ln 8 > 4 n \ln 52 + 3 \ln 52$

$- 3 \ln 52 > 4 n \ln 52 - 2 n \ln 8$

$- 3 \ln 52 > 2 n \left(2 \ln 52 - \ln 8\right)$

$\frac{- 3 \ln 52}{2 \ln 52 - \ln 8} > 2 n$

$- 1.0178 > n$

Hopefully this helps!