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Logarithmic Expressions: Difficult Problems with Solutions

By Catalin David
Problem 1 sent by V. Pavan Kaarthikeya
If $(a+b)^2=4ab$
Is it true that
$\log(a^2+b^2)=2\log (a) +2\log(b)$
Problem 2
Find the value of the logarithm: [tex]log_{2\sqrt[3]{2}}\frac{1}{16} = ?[/tex]
Problem 3
Find the value of the logarithm: [tex]log_{\frac{1}{8}}\sqrt[4]{32} = ?[/tex]
Problem 4
Find the value of the logarithm: [tex]log_{\frac{1}{8}}0.25 = ?[/tex]
Problem 5 sent by Mehdi Ahangareianabhari
If [tex]log4, log(2^x+2)[/tex] and [tex]log(2^{x+2}+1)[/tex] are the three items of an arithmetic progression, find x?
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