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If f(x)=log (base a) x, show that f(x^a)=a f(x)

2007-12-09 08:28:25 · 2 answers · asked by star baller 360 5 in Science & Mathematics ➔ Mathematics

f(x)=log (base a) x
f(x^a)=log (base a)(x^a)

Using the rule

log (x^a) = a log ( x )

yields

a log (base a) x = a f(x)

2007-12-09 08:34:24 · answer #1 · answered by jgoulden 7 · 1⤊ 0⤋

f(x^a)=log (base a) x^a=a(log (base a) x)=a f(x)

2007-12-09 08:35:44 · answer #2 · answered by Adrian R 1 · 1⤊ 0⤋