Prove That: $$ 3^{\log_3\sqrt {x-1}} <3^{\log_3{(x-6)}} + 3 $$
My Try At It: I first took the 3 common and then converted the whole question $$ 3^{\log_3\sqrt {(x-1)}} <3^{\log_3{(x-6)}} + 3 $$ into a logarithamic one but at the end I got stuck.
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1Do you know that $3^{\log_3 a}=a$? – Crostul Apr 13 '17 at 11:47
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1thanks for it. i forgot bout that one – Esha Mukhopadhyay Apr 13 '17 at 11:49
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I particularly loved the "my try at it" part ! – Zubzub Apr 13 '17 at 11:53
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is it $$3^{\log_3 x-6}$$ or $$3^{\log_3 (x-6)}$$? – Dr. Sonnhard Graubner Apr 13 '17 at 11:53
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1i solved it. thanks. the second one is correct – Esha Mukhopadhyay Apr 13 '17 at 11:55
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@EshaMukhopadhyay I edited your post. Is this what you meant? – Arbuja Apr 13 '17 at 12:20