Question

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

Answer 1

Answer:

256

Step-by-step 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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