Question

Show that log 360=3 log2 + 2 log3 + log5​

Answer 1

Step-by-step explanation:

log 360

Prime factorization 360

We write 360= 2^3 ×3^2 ×5

or, log 360

= log (2^3 ×3^2 ×5

Using log (a x b x c) = log a +log b +log c

= log 2^3 +log 3^2 + log 5

Using log a^b = b log a

we write,

= 3 log 2 + 2 log 3 + log 5. (=RHS)

Hence proved.

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