Question

simplest form of log16-2log2​

Answer 1

hence simplest form of log(16) - 2log(2) = log(4)

It is given that, log(16) - 2log(2)

we have to use some important logarithm concepts

• logaⁿ = n loga .......(1)
• loga - logb = log(a/b)......(2)
• n loga = logaⁿ ..........(3)

log(16) = log(2 × 2 × 2 × 2)

= log(2⁴)

= 4log2 [ from concept (1) ]

now, log(16) - 2log(2)

= 4log(2) - 2log(2)

= 2log(2)

= log(4) [ from concept (3) ]

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Answer 2

The Simplest form of $log(16)-2log(2)$ is $log(4)$

Step-by-step explanation:

Given,

Simplest from of $log(16)-2log(2)$

∴ $log(16)-2log(2)$

$=log(2^{4})-2log(2)$

$=4log(2)-2log(2)$ (∵$loga^{n} = n log(a)$)

$=2log(2)$

$=log(2^{2})$

$=log(4)$

So, The Simplest form of $log(16)-2log(2)$ is $log(4)$