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What is log base 5(4*7 )+log base 5 of 2 written as a single log?
A.log base 5 of 21
B.log base 5 of 26
C.log base 5 of 30
D.log base 5 of 56

Respuesta :

carlosego
The answer for the exercise shown above is the last option (Option D), which is:

 D. log base 5 of 56

The explanation is show below:

 1. You have the following logarithm expresssion:

 log5(4*7 )+log5(2)

 2. By the logarithms properties, you can rewrite the logarithm expression as following:

 log5(28)(2)
 log5(56)

 3. Therefore, as you can see, the answer is the option mention before.
 

Answer:

D. log base 5 of 56

Step-by-step explanation:

Since, by the multiplication law of logarithm,

[tex]log_a(m)+log_a(n) = log_a(mn)[/tex]

Given expression is,

log base 5(4*7 )+log base 5 of 2

[tex]=log_5(4\times 7)+log_5(2)[/tex]

[tex]=log_5(28)+log_5(2)[/tex]

By the above property,

[tex]=log_5(28\times 2)[/tex]

[tex]=log_5(56)[/tex]

= log base 5 of 56

Hence, Option D is correct.

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