Question

Express log^2A in terms of the logarithms of prime numbers

Answer 1

Solution

$A=\frac{\sqrt[]{3}\sqrt[4]{125}}{7^3}$

And we want to find log_2 A and we can do this :

$\log _2A=\frac{1}{2}\log _2(3)+\frac{3}{4}\log _2(5)-3\log _2(7)$

And the reason is because:

$\log _2(\sqrt[4]{125})=\log _2(\sqrt[4]{25\cdot5})=\log _2(\sqrt[4]{5^3}))=\frac{3}{4}\log _2(5)$