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ASHA 777 [7]
3 years ago
10

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

Mathematics
2 answers:
stepladder [879]3 years ago
8 0

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.

alina1380 [7]3 years ago
7 0

\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}}

<u>Or</u><u>,</u><u> </u>

➙ log₂(256) = log₁₀(256) / log₁₀(2)

➙ log₂(256) = 2.40823996531 / 0.301029995664

➙ log₂(256) = 8

☕️ Hence, solved !!

<u>━━━━━━━━━━━━━━━━━━━━</u>

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Given:

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From the given graph, it is clear that the exponential function passes through the points (1,1) and (3,9). So, the equation of the exponential must must be satisfy by these points.

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