Question

Express each logarithm in terms of In 2 and In 5.

Answer 1

Answer:

$5ln2-3ln5$

$2ln5-ln2$

Step-by-step explanation:

∵ $32=2^{5}$

∵ $125=5^{3}$

∵ $ln\frac{32}{125}=ln\frac{2^{5}}{5^{3}}$

∴ $ln2^{5}-ln5^{3}=5ln2-3ln5$

∵ $12.5=\frac{125}{10}=\frac{25}{2}=\frac{5^{2}}{2}$

∴ $ln12.5=ln\frac{5^{2}}{2}$

∴ $ln5^{2}-ln2=2ln5-ln2$