Need a clarify

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Madu

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Question is 2log10^5 + log10^4 is equal to
Select one or more:
Answers are
a. 2
b. 2(log10^5 + log10^2)
c. 2log10 ^(5 + 4)
d. log10 ^25 + 2log10 ^2
e. 2log10 ^(5 × 4)

I know the answer is a.This question says "is equal to", so I'm confused that I should choose exactly the answer means "a" or can I choose b and d too, Can anyone clarify this.
 
If you are even close to correct as to what the question really asked, then option a is not the correct answer. Why do you think it is? What is your reasoning with respect to b and to d?
 
Screenshot_2020-11-24_234131.jpg

This is the question, so a is a definitely a answer right? I'm confused about b and d
 
I already told you that option a is NOT correct. How did you reach that conclusion?

What is your reasoning with respect to b, c, d, and e.
 
There are many ways to say the same value so multiple answer can be correct. For example 4 is equal to 2*2, 4 is equal to 2^2 is equal to 4 = 5-1
 
Madu said:
Question is 2log10^5 + log10^4 is equal to
Select one or more:
Answers are
a. 2
b. 2(log10^5 + log10^2)
c. 2log10 ^(5 + 4)
d. log10 ^25 + 2log10 ^2
e. 2log10 ^(5 × 4)

I know the answer is a.This question says "is equal to", so I'm confused that I should choose exactly the answer means "a" or can I choose b and d too, Can anyone clarify this.
Click to expand...
Since no one else has said this explicitly, I'll do so. Your notation here is totally wrong, and probably misled at least one person.

log10^4 is [MATH]\log(10^4) = \log(10000) = 4[/MATH].

What the problem actually has is [MATH]\log_{10} 4[/MATH], which would be typed as log_10(4). The 4 is not an exponent; rather, the 10 is a subscript.

Given the actual problem, which asks you to rewrite [MATH]2\log_{10}5 + \log_{10}4[/MATH], you are correct about (a), but (b) is also equal. Simplifying yields [MATH]2\log_{10}5 + \log_{10}4 = \log_{10}5^2 + \log_{10}4 = \log_{10}(5^2\cdot 4) = \log(100) = 2[/MATH]. But similarly, [MATH]2(\log_{10}5 + \log_{10}2) = 2\log_{10}10 = 2[/MATH]. See if anything else also has the same value!
 
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