Easy Exponents

Algebra Level 1

If 9 3 − x = 81 4 − 2 x { 9 }^{ 3-x }={ 81 }^{ 4-2x } , then what is x ? x?

5 3 \frac{5}{3} 3 5 \frac{3}{5} − 3 5 -\frac{3}{5} 7 6 \frac{7}{6}

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Isaiah Simeone by isaiah simeone , 23, Australia

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26 solutions

Isaiah Simeone
Sep 25, 2014

9 3 − x = 81 4 − 2 x { 9 }^{ 3-x }={ 81 }^{ 4-2x }

9 3 − x = 9 8 − 4 x { 9 }^{ 3-x }={ 9 }^{ 8-4x }

3 − x = 8 − 4 x 3-x=8-4x

5 = 3 x 5=3x

x = 5 3 x=\frac { 5 }{ 3 }

141 Helpful 0 Interesting 1 Brilliant 0 Confused

I did this using logarithms: 9^3-x=81^4-2x is equivalent to (3-x)log9(9)=(4-2x)log9(81) which if you simplify the logs, 3-x=2(4-2x) which can be simplified for an answer of x=5/3

Jason Lee - 6 years, 8 months ago

Elementary exponent rules

Prakash Moghe - 6 years, 8 months ago

it is the interesting question l like

tayyab bashir - 6 years, 8 months ago

I love this topic

Brenda Joyce Jamil - 6 years, 8 months ago

elementary exponential problem

parth tandon - 6 years, 8 months ago

I also solved it the same as you did

Ahmed Obaiedallah - 6 years ago

But I did the opposite :
9^(3-x) = 81^(4-2x)
9^(2)^(3-x) =81^(4-2x)
9^(6-2x) =81^(4-2x)
6-2x = 4-2x
6 don't equal 4 What's the problem

abd alrahman kandil - 5 years, 9 months ago

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أنت إزاى ربعت الـ 9 اللى على الشمال !! أنت كده غيرت المعادلة خالص

لو أنت عايز تحول الـ 9 و تجعلها 81 هتخليها 81 أس 0.5 أو الجذر التربيعى ل، 81 لأنها فى الاساس 9 مش 81

If want to work at the left hand side instead you should have done it as follows

9 3 − x = 8 1 4 − 2 x \Large9^{3-x}=81^{4-2x}

8 1 1 2 × ( 3 − x ) = 8 1 4 − 2 x \Large81^{\frac12\times(3-x)}=81^{4-2x}

1 2 × ( 3 − x ) = 4 − 2 x \Large\frac12\times(3-x)=4-2x

3 − x = 2 × ( 4 − 2 x ) \Large3-x=2\times(4-2x)

3 x = 5 \Large3x=5

x = 5 3 \Large x=\frac53

Ahmed Obaiedallah - 5 years, 9 months ago

you only sqaured one side of the equation. what you do to one side, you must also do to the other

Adam Ecker - 5 years, 1 month ago

it's so easy

Mohamed Eltayeb - 6 years, 8 months ago

So far, the easiest solution.

Michel Lerqué - 6 years, 8 months ago

it's very easy question!

Engr Milon Howlader - 6 years, 8 months ago

i had to think a little bit, but made it out last :)

Rostam Dana - 6 years, 8 months ago

Simple yet interesting....

has kh - 6 years, 8 months ago

It was very easy and interesting too..!!

Anagha Nair - 6 years, 8 months ago

same like the australian said

SvEn Tavas - 6 years, 8 months ago

I am unable to understand how the bases(9's) were removed?

avi singhal - 6 years, 4 months ago

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You can eliminate the bases when they are the same in an equation like the one given in the problem

Jazz Nash - 5 years, 10 months ago

81 to the fourth power and 9 to the eighth power are equivalent. so you drop the 9's since they cancel each other when dividing. I think that's what you were looking for.

Kyle Bambenek - 5 years, 10 months ago

The bases are still there, but when trying to balance out both sides of the equation and the bases are identical (in this case the 9), then we know that the powers (and the quantities attached to them) have to equal out to the same quantity. Then, you set up an equation to solve for the variable attached as the power expression.

Eric Beck - 5 years, 2 months ago

why X is not power 2 although solution made 4 and 2 in thz equ 4-2X .. ?!

Tunex Tawkel - 5 years, 11 months ago

I got the same solution!1 so easy..............

Julie Ann Arenilla - 6 years, 8 months ago
Mec Bal
Oct 1, 2014

To equate powers, its mandatory that base should be same. So RHS can be rewritten as 9^2(4-2x), which is 9^(8-4x) . Now equate with LHS. 9^(3-x) = 9^(8-4x) ==> 3-x = 8-4x ==> 4x-x=8-3 ==> 3x=5 ==> "x=5/3 "

8 Helpful 0 Interesting 0 Brilliant 0 Confused

did the same

Karthik Rocks - 6 years, 7 months ago
Tooba Rana
Oct 2, 2014

I am bad at maths but I am glad that I did it..!! it's sooo easy man..!! :)

4 Helpful 0 Interesting 0 Brilliant 0 Confused

`Yet someone still voted you haha.

Steven Sison - 6 years, 1 month ago
Manish Sharma
Sep 27, 2014

taking log base 9 both side so 3-x=8-4x

2 Helpful 0 Interesting 0 Brilliant 0 Confused

this is the easy way to get exact answer

Prabu Chandran - 6 years, 8 months ago

so easy 5/3

Gebremedhin Hagos - 6 years, 8 months ago
Vishal S
Dec 14, 2014

We can write 9^3-x=81^4-2x as 9^3-x=9^2(4-2x)

=>9^3-x=9^8-4x

since bases are same, we can compare the powers

=>3-x=8-4x

=>4x-x=8-3

=>3x=5

=>x=5/3

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramesh Jat
Sep 30, 2014

first make the base equal .when bases r equal automatically power r also equal 3-x=2(4-2x) 3-x=8-4x -x+4x=8-3 3x=5 x=5/3

1 Helpful 0 Interesting 0 Brilliant 0 Confused

its been a while

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ngọc Nguyễn
Sep 28, 2014

<=> 9^(8-4x)= 9^(3-x) <=> [9^(8-4x)]/ [9^(3-x)]=1 <=> 8-4x-3+x=0 <=> 5-3x=0 <=> x=5/3

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ajay Sutradhar
Sep 27, 2014

3-x=2(4-2x)

3-8=-4x+x

-5=-3x

x=5/3

1 Helpful 0 Interesting 0 Brilliant 0 Confused

How did you get 2(4-2x) from 81^4-2x?

Robbie Isbell - 5 years, 11 months ago

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81 is the square of 9.. Hence,81^(4-2x) becomes 9^2 (4-2x) which further becomes 9^(8-4x)

Anwesha Sinha - 5 years ago
Anwesha Sinha
Jun 7, 2016

9^(3-x)=81^(4-2x)

9^(3-x)=9^2(4-2x)

9^(3-x)=9^(8-4x)

Since the base is equal, hence,

3-x=8-4x

3-8=-4x+x

-5=-3x

5=3x

5/3=x

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ajin Varghese
Dec 31, 2015

Agreed with isaiah simeone

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Hadia Qadir
Aug 4, 2015

9^(3-x) = 9^(8-4x) Since same bases

3-x = 8-4x 4x-x = 8-3 3x=5 x=5/3

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Sneha Dey
Jul 21, 2015

Write a solution. 3-x=8-4x 5-3x=0 5=3x x=5/3

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Krishna Garg
Jun 27, 2015

We can write the given expression as 9^3-x =81^4-2x as 9^3-x =9^2(4-2x) Therefore 3-x = 2(4-2x), by solving this equation we get x = 5/3 Ans

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Princess Mano
Jan 1, 2015

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Harsh Rathore
Nov 5, 2014

Juzt make base equal

0 Helpful 0 Interesting 0 Brilliant 0 Confused

9^3-x=9^2(4-2x) bases r equal so, 3-x=8-4x 3x=5 x=5/3

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Sara D
Oct 13, 2014

If you can recognize that 81 is the square of 9 then the right hand expression becomes 9 to double the current exponent so 8 - 4x ... set the two exponents equal and solve to get x = 5/3

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Rahul Chudasama
Oct 11, 2014

9^3-x = 81^4-2x--> 9^3-x = 9^2(4-2x)--> 3-x = 2(4 -2x).....................(If a^m = a^n then m = n)--> 3-x = 8-4x--> 4x-x = 8-3--> 3x = 5--> x = 5/3.

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Soomro Khan
Oct 6, 2014

9^3-x=81^4-2x......... 9^3-x=9^2(4-2x).............. 9^3-x=9^8-4x................ here bases r same then we can qual their powers so, 3-x=8-4x.......... by replacing variables and constants we get, 3x=5..... then x=5/3

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Darshan Kamaliya
Oct 2, 2014

3-x=2(4-2x) X=5/3 Take log both side (3-x)log(9)=(4-2x)log(9^2)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice trick

Saurabh Kumar - 6 years, 8 months ago
Omar Agour
Sep 29, 2014

_ 3-x=2(4-2x) _ 3-x=8-4x _ -5=-3x _ x=5/3 _ :)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

3-x=8-4x 5=3x x=5/3

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Sobia Parveen
Sep 28, 2014

9^(3-x)=81^(4-2x) Taking square on both sides 81^(3-x)=81^(8-4x) or 3-x=8-4x or -x+4x=8-3 or 3x=5 or x=5/3

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Ana Clara Reis
Sep 28, 2014

9^{3-x}= (9^{2})^{4-2x} 3-x= 2*(4-2x) 3-x= 8-4x x= 5/3

0 Helpful 0 Interesting 0 Brilliant 0 Confused

u r brilliant

Ragul Bcs - 6 years, 8 months ago
Sonu Raj
Sep 28, 2014

9^3-x=81^4-2x or,9^3-x=9^8-4x or,3-x=8-4x or,3-8=-4x+x or,-5=-3x or,5=3x so x=5/3

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