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zlopas [31]
3 years ago
9

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

Mathematics
1 answer:
Sladkaya [172]3 years ago
3 0

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

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