Question

log 3600 is equals to??​

Answer 1

Answer:

Log 3600 is equal to a 2log6 1 b 6log2 1 c 2log6 2 d 6log2 2.

Answer 2

To find:

A simplified form of $log(3600)$

Let us know some rules:

Before we solve problems related to $logarithm$, we write down some rules,

• $log_{a}(MN)=log_{a}(M)+log_{a}(N)$

• $log_{a}(M\div N)=log_{a}(M)-log_{a}(N)$

• $log_{a}(a)=1$

• $log_{a}(M^{n})=n\:log_{a}(M)$

Step-by-step explanation:

Now, $log(3600)$

$=log(2\times 2\times 2\times 2\times 3\times 3\times 5\times 5)$

• We have prime factorized $3600$.

$=log\{(2\times 2\times 3\times 5)^{2}\}$

$=log(60^{2})$

$=2\log 60$, since $log_{a}(M^{n})=n\:log_{a}(M)$

Answer: $log(3600)=2\:log(60)$

Extra:

Further the expansion becomes,

$\quad log(3600)$

$=2\:log(60)$

$=2\:log(2^{2}\times 3\times 5)$

$=2\:\{2\:log(2)+log(3)+log(5)\}$

$=4\:log(2)+2\:log(3)+2\:log(5)$

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