Logarithm simplification Simplify: \(\displaystyle{{\log}_{{4}}{\left(\sqrt{{{2}+\sqrt{{{3}}}}}+\sqrt{{{2}-\sqrt{{{3}}}}}\right)}}\) Can we use the formula

r1fa8dy5

r1fa8dy5

Answered question

2022-03-21

Logarithm simplification
Simplify: log4(2+3+23)
Can we use the formula to solve this: a+b={a+a2b}2
Therefore first term will become: 12
log4 can be written as 12log2
Please guide further..

Answer & Explanation

Esteban Sloan

Esteban Sloan

Beginner2022-03-22Added 21 answers

Let x=2+3+23
x2=(2+3)+(23)+2(2+3)(23)=6
I think you get it from here.
Mason Knight

Mason Knight

Beginner2022-03-23Added 11 answers

2+3=4+232=(3)2+12+2312=(3+1)22
So,2+3=3+12
Similarly,  23=312

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