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I made a mistake in the title of this thread and this question is on general logarithms;

log

_{a}(a

^{loga(x)}) = log

_{a}(x) ==> a

^{loga(x)}= x

Can someone enlighten me on why log

_{a}(a

^{loga(x)}) simplifies to log

_{a}(x)? Can someone prove why this is true? Futhermore, why does this imply that a

^{loga(x)}= x? I am having trouble getting my head around this

Sincerely,

Bardagath