If log25 ~ 2.3219,
evaluate log280.

Answers

Answer 1

Answer:

You need to write log_2 80 in terms of log_2 5 , such that:

log_2 80 = log_2 (8*10)  

Using the properties of logarithms, you need to convert the logarithm of product in summation of logarithms, such that:

log_2 (8*10)= log_2 8 + log_2 10

Since log_2 10 = log_2 (2*5) , yields:

log_2 (8*10)= log_2 8 + log_2 (2*5)

log_2 (8*10)= log_2 8 + log_2 2 + log_2 5

You need to write 8 as power of 2, such that:

log_2 (8*10) = log_2 (2^3) + log_2 2 + log_2 5

Using the power property of logarithms, log_a b^c = c*log_a b  yields:

log_2 (8*10) = 3log_2 2 + log_2 2 + log_2 5

Since log_2 2 = 1 yields:

log_2 (8*10) = 3 + 1 + 2.3219

log_2 (8*10) = 4 + 2.3219 => log_2 (8*10) = 6.3219

Hence, evaluating the given logarithm , using the indicated properties of logarithms, yields log_2 (8*10) = 6.3219 .

Step-by-step explanation:

Answer 2

The value of [tex]log_2{80}[/tex] if [tex]log_25 = 2.3219[/tex] is 6.3219.

What is a logarithm?

The logarithm is exponentiation's opposite function in mathematics.

This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.

Given, [tex]log_25 = 2.3219[/tex].

Now, To obtain the value of [tex]log_2{80}[/tex] we'll break it into suitable smaller parts.

Therefore,

[tex]log_2{80} = log_2({8\times10})[/tex].

[tex]log_2{80} = log_28 + log_210[/tex]

[tex]log_2{80} = log_28 + log_2({2\times5})[/tex].

[tex]log_2{80} = log_28 + log_22 + log_25[/tex].

[tex]log_2{80} = 3 + 1 + 2.3219[/tex].

[tex]log_2{80} = 6.3219[/tex].

learn more about logarithms here :

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Answers

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Step-by-step explanation:

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Answers

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