Question

look at the attachement and the problems asked in it

Answer 1

$log_{10}\ 2=a\\log_{10}2*5=1=>a+log_{10}\ 5=1\\log_{10}5=1-a$
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$log(x^2y^3)=2\ Log\ x+3\ log\ y=9\\\\Log\ x-Log\ y=2\\\\Solving\ two\ equations\\\\5\ log\ x=15\\log\ x=3\\log\ y=1$
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$multiply\ all\ three.\\log_a\ b *log_b\ c\ *\ log_c\ a=1\\since\ all\ three\ are\ equal,\ each=1\\a=b=c$
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$x^{2x+1}\ *\ 4^{x-1}=36\\\\x^{2x+1}*2^{2x}=2^4*3^2=144\\\\(2x+1)log_2\ x+2x=Log_2\ 144\\2x\ log_2\ 2x+log_2\ 2x-1=144\\(2x+1)log_2\ 2x=145\\?????$
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$log_a\ 10^{-2}=2\ log_x\ 10=z(say)\\\\a^z=10^{-2}\\x^z=100=\frac{1}{a^z}\\\\=>x=\frac{1}{a}$
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as log value is zero, it means the value of operand is 1.
$Log_2\ (log_4\ (x-15))=1\\\\Log_4\ (x-15)=2\\\\x-15=16\\\\x=31$