Question

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

Answer 1

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

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

`\log _2A=(1)/(2)\log _2(3)+(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}))=(3)/(4)\log _2(5)`