Can someone simplify this?sqrt(4log2+(log5)^2)+sqrt(4log5+(log2)^2)

jhenezhubby01ff

jhenezhubby01ff

Answered question

2022-09-07

Need to simplify a logarithmic expression
Can someone simplify this ( log here refers to the common logarithm)?
4 log 2 + ( log 5 ) 2 + 4 log 5 + ( log 2 ) 2
I know this has a simple solution but I cannot find it.

Answer & Explanation

Samantha Braun

Samantha Braun

Beginner2022-09-08Added 9 answers

It seems pretty sneaky. So I'm guessing those are common logs. Let's take a look at the first square root. We have
4 log 2 + ( log 5 ) 2 = 4 ( log 10 log 5 ) + ( log 5 ) 2 = 4 4 log 5 + ( log 5 ) 2 = 2 log 5
Similarly, the second square root yields 2 log 2. Sum them together to get 4 log 10 = 3

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