An algebra problem by Dominick Hing

Algebra Level pending

Let f ( x ) = e 2 x f(x)={ e }^{ 2x } and g ( x ) = ln ( x ) g(x)=\ln { (x) } . Evaluate f ( g ( 7 ) ) f(g(7)) .

49 48 14 7

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1 solution

Dominick Hing
Sep 27, 2014

f ( g ( 7 ) ) = e 2 ln 7 = e ln ( 7 2 ) = e ln 49 = 49 f(g(7))\quad =\quad { e }^{ 2\ln { 7 } }={ e }^{ \ln { ({ 7 }^{ 2 }) } }={ e }^{ \ln { 49 } }=49

e 2 ln 7 = e ln ( 7 2 ) { e }^{ 2\ln { 7 } }={ e }^{ \ln { ({ 7 }^{ 2 }) } } because you can move the number in front of the natural log to the exponent above the argument (power rule).

e ln 49 = 49 { e }^{ \ln { 49 } }=49 because the e raised to the natural log of any number is that number

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