Module'2'Lesson'3'
Solving'Exponential'and'Logarithmic'Equations''
Notes'Part'2'Video'1'Transcript'
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!Hey!everyone,!this!is!a!video!for!module!2!lesson!3,!solving!exponential!and!
logarithm!equations.!!We!are!in!the!notes!part!2.!!
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So!we!are!going!to!look!at!some!examples!about!solving!for!x.!!So!the!first!one!says,!
solve!for!x.!!So!we!need!to!get!this!x!by!itself,!so!the!first!thing!that!we!need!to!do!
here!is!subtract!a!4.!!And!that!would!leave!8!to!the!3x!would!equal!3.!!Now,!to!
continue!to!get!x!by!itself!I!am!going!to!change!this!to!logarithmic!form.!!And!
changing!that!to!logarithmic!form!would!look!like!the!log!base!of!8!of!3!would!equal!
3x.!!So!the!log!of!8!and!that!3!equals!the!exponent.!!So!to!get!the!number,!or!to!solve!
for!x!I!would!have!to!divide!both!sides!by!3.!!So!this!means!that!x!would!equal!the!log!
base!8!of!3!over!3,!which!to!put!that!in!the!calculator!I!would!have!to!do!the!change!
of!base.!!So!it!would!be!the!log!of!3!over!the!log!of!8!all!of!that!divided!by!3.!!So!I!am!
going!to!pull!my!calculator!up!here!and!put!that!in.!!I!have!to!put!the!entire!
numerator!in!parenthesis,!so!I!have!the!log!of!3!divided!by!the!log!of!8,!close!my!
parenthesis!around!the!8!and!the!3,!and!I!close!another!parenthesis!around!the!
numerator!and!I!divide!by!3.!!I!would!get!that!x!is!approximately!.1761.!!So!the!
answer!for!x!in!this!problem!is!approximately!.1761.!!Round!your!answer!to!4!
decimal!places.!!On!these!types!of!problems!remember!to!check!your!answer!just!to!
save!time!on!the!video!I!know!that!is!the!correct!answer!so!we!are!just!going!to!
move!on!but!make!sure!you!check!your!answers!when!you!are!working!by!yourself.!!
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All!right!the!next!problem!says!L4!to!the!negative!x!plus!7!minus!5!equals!L14.!!So!to!
start!getting!x!by!itself!first!I!am!going!to!add!5!to!both!sides.!!Adding!5!to!that!would!
give!me!L9.!!Then!I!am!going!to!divide!by!L1.!!So!that!would!give!me!4!to!the!–x!plus!7!
would!equals!9.!!Now!I!am!going!to!change!that!to!logarithmic!form!so!I!would!have!
the!log!base!4!of!9!equals!–x!plus!7.!!So!to!get!the!x!by!itself!I!am!going!to!subtract!7!
from!both!sides.!!And!then!I!would!divide!by!L1,!so!that’s!going!to!be!negative!log!
base!4!of!9!plus!7!would!equal!x.!!So!to!put!that!in!the!calculator!I!would!have!to!do!
the!change!of!base.!!So!the!negative!log!of!9!over!the!log!of!4!plus!7!would!go!in!for!x.!!
So!I!would!put!that!in,!and!I!would!put!negative!log!of!9!divided!by!log!of!4!and!I!
would!do!that!first!and!then!add!7!and!I!get!x!is!approximately!5.4150.!!!So!once!
again!check!your!answers!when!you!are!working!by!yourself,!but!that!is!the!correct!
answer!for!this!one.!!
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Ok,!the!next!piece!or!the!next!problem,!we!have!5!raise!to!the!x!squared!equals!5!to!
the!7th.!!So!looking!at!this!you!notice!that!these!bases!are!the!same.!!So!if!these!bases!
are!the!same!that!means!their!exponents!are!the!same.!!So!x!squared!would!have!to!
equal!the!value!of!7!so!to!solve!for!x!I!would!square!root!both!sides!I!would!have!
plus!or!minus!(positive!or!negative),!so!that!would!become!x!equals!plus!or!minus!
the!square!root!of!7.!!Once!again!check!your!answer!when!you!are!doing!these!by!
yourself,!but!you!have!those!answers!there.!!
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Ok,!number!4!looks!a!little!bit!different,!kind!like!the!last!one.!!We!have!a!3!here!and!
a!27!here!(underlining!the!bases).!!Those!bases!are!not!the!same!but!with!a!little!
manipulation!we!can!make!them!be!the!same.!!So!if!you!notice!27!I!could!rewrite!
that!to!be!3!to!the!3rd.!!So!I!could!rewrite!that!as!3!to!the!3rd,!raised!to!the!5x!minus!
7.!!What!that!allows!me!to!do!it!get!a!power!to!a!power!here.!!So!I!could!leave!this!
the!same,!3!raised!to!the!2x,!and!this!could!become!3!and!that!power!times!that!
power!would!be!15x!minus!21!because!you!would!have!to!distribute!the!3!through!
there,!so!now!you!could!set!their!exponents!to!equal!each!other,!so!2x!equals!15x!
minus!21.!!And!solve!for!x!I!would!subtract!15x!from!both!sides!so!L13x!would!equal!
L21.!!!
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And!dividing!by!L13!on!both!sides!you!would!get!x!equals!21!over!13!and!that!would!
be!your!answer.!!!And!I!checked!that!one!as!well.!!Once!again!when!you!are!doing!
these!by!yourself!just!make!sure!you!are!not!making!any!mistakes!down!here,!and!
one!way!to!make!sure!of!that!is!to!just!check!your!answers.!!
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Here!we!have!the!number!”e.”!!We!have!“e”!raised!to!the!3x!squared!equals!“e”!
raised!to!the!8th!power.!!!So!here!we!have!the!same!base!so!we!can!go!ahead!and!set!
the!powers!equal!to!each!other.!!3x!to!the!second!would!equal!8.!!To!solve!for!x!I!
would!divide!by!3!and!then!you!can!square!root!that.!!So!if!you!square!root!that,!it!
would!be!plus!or!minus!the!square!root!of!8!over!3.!!So!you!can!check!those!answers!
as!well.!
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