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Module!2!Lesson!2!
Exponential!and!Logarithmic!Functions!!
Changing!from!Form!to!Form!and!Evaluating!Equations!Video!1!Transcript!
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Hey$everyone$this$is$a$video$for$module$2$lesson$2,$exponential$and$logarithmic$
functions.$$We$are$in$the$notes$part$1$and$in$this$video$I$will$be$changing$from$form$to$
form$and$evaluating$equations.$
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So!the!first!set!of!directions!says,!change!each!exponential!form!to!logarithmic!form.!!
So!as!you!seen!in!the!notes,!to!change!an!exponential!form,!which!is!something!that!
has!an!exponent!to!logarithmic!form,!you!do!this.!!You’re!going!to!have!a!base!raised!
to!the!x!power,!equals!another!number!or!a!variable!in!some!cases.!!And!how!change!
that!is!you!go!log!and!then!that!base!becomes!a!little!number!down!here,!the!“y”!
become!this!part,!and!that!going!to!equal!the!exponent.!!
So!if!I!am!in!exponential!form!to!get!to!logarithmic!form,!I!am!going!to!write!log!and!
since!our!base!on!exponential!form!is!3,!that!is!going!to!be!a!small!3!down!there,!
then!the!81!comes!over!here!with!the!log!and!that!is!going!to!set!equal!to!the!
exponent.!!So!that!exponential!form,!is!this!logarithmic!form.!Those!are!equivalent!
statements,!just!different!ways!to!write!them.!!
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So!5!to!the!third!equals!125,!so!if!I!put!that!in!logarithmic!form,!you!do!log!base!5!of!!
125!would!equal!3.!
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!To!put!7!to!the!x!power!equals!9!into!logarithmic!form,!it!would!become!log!base!7!
of!9!equals!x,!which!is!the!exponent.!!
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And!number!4!it!would!be!log!base!4!of!24!would!equal!the!x.!
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Ok!so!for!the!next!set!of!directions,!its!going!to!say,!change!each!logarithmic!form!to!
exponential!form.!!So!now!I!am!going!to!work!backwards,!so!now!if!I!have!log!base!2!
of!8!equals!3,!I!am!going!to!change!that!back!to!exponential!form,!so!that!is!going!to!
be!2!raised!to!the!third!power!would!equal!8.!!So!that!is!the!equivalent!exponential!
form.!
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Number!6!says!log!base!6!of!36!equals!2,!so!you!are!going!to!do,!6!raised!to!the!
second!power!equals!36.!!
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Number!7,!we!have!log!of!x!equals!3,!it!was!discussed!in!your!notes!but!if!I!do!not!
have!a!base!down!here!in!my!logarithmic!equation,!then!that!is!an!understood!10!
base.!!So!to!put!this!in!exponential!form,!it!would!be!10,!because!there!is!an!
understood!10!here,!raised!to!the!third!power!would!equal!x.!!
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And!for!the!last!one!log!base!5!of!x!equals!3.!!That’s!going!to!be!5!raised!to!the!third!
power!equals!x.!
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Now,!the!next!set!says!to!solve!for!x.!!So!we!have!log!base!4!of!16!equals!x.!!So,!if!I!
have!something!like!this,!I!know!that!an!equivalent!statement!to!this!would!be!4!
raised!to!the!x!power!would!equal!16.!!Now!on!this!set!of!problems,!we!are!going!to!
be!able!to!do!these!in!our!head.!!So!4!raised!to!something!has!to!equal!16.!!So!x!
would!have!to!equal!2!because!4!squared!is!16.!!!
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On!number!10,!once!again!we!have!log!base!8!of!64!equals!x,!so!I!can!rewrite!that!to!
say!8!to!the!x!power!would!equal!64.!!And!doing!that!in!our!head,!x!would!equal!2!as!
well.!!!
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Number!11,!log!base!3!of!27!equals!x,!that!would!be!equivalent!to!3!raised!to!the!x!
power!equals!27.!!Then!ask!yourself,!3!raised!to!what!power!would!give!you!27,!and!
that!would!be!x!equals!3.
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And!to!change!number!12,!you!would!have!4!raised!to!some!power!equals!1.!!
Therefore,!x!would!have!to!equal!0,!because!4!raised!to!the!0!power!would!be!
equivalent!to!1.!
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And!that’s!how!you!change!from!form!to!form,!and!evaluate!some,!when!it!says!to!
solve!for!x.!!