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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: $$log_{2\sqrt[3]{2}}\frac{1}{16} = ?$$
Problem 3
Find the value of the logarithm: $$log_{\frac{1}{8}}\sqrt[4]{32} = ?$$
Problem 4
Find the value of the logarithm: $$log_{\frac{1}{8}}0.25 = ?$$
Problem 5 sent by Mehdi Ahangareianabhari
If $$log4, log(2^x+2)$$ and $$log(2^{x+2}+1)$$ are the three items of an arithmetic progression, find x?
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