Question

Evaluate. log (down)2 256 . Write a conclusion statement.

Answer 1

256

Explanation:

log 256 can most easily be found by rewriting 256 as a power of 2:

2

2^5 * 2^3 = 32*8 = 256, so 2^ (5 + 3) = 2^8.

Then we have:

log 256

2 2 = 256

Alternatively, write:

log (down)2 256 = log (down)2 2^8 = 2*8 = 256

Note that your "log (down)^2 and the function y = 2^x are inverse functions that effectively cancel one another.

Answer 2

`\Large{ \boxed{ \bf{ \color{blue}{Solution:}}}}`

By using the fact that,

When,

`\large{ \sf{ {a}^(x) =b}}`

Then, With logarithm base a of a number b:

`\large{ \sf{ log_(a)(b) = x}}`

☃️So, Let's solve ths question....

To FinD:

`\large{ \sf{log_(2)(256) }}`

Let it be x,

`\large{ \sf{ \longrightarrow{ log_(2)(256) = x}}}`

Proceeding further,

`\large{ \sf{ \longrightarrow \: {2}^(x) = 256}}`

`\large{ \sf{ \longrightarrow \: {2}^(x) = {2}^(8) }}`

Then, We have same base 2, So

`\large{ \sf{ \longrightarrow \: x = 8}}`

Or,

➙ log₂(256) = log₁₀(256) / log₁₀(2)

➙ log₂(256) = 2.40823996531 / 0.301029995664

➙ log₂(256) = 8

☕️ Hence, solved !!

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