Solve 3^(4x+1) - 2*3^(2x+2) = 81

Sundar Kumar   10 years AGO

3^(4x+1) - 2*3^(2x+2) = 81
3^4x*3-2*3^2x*3^2=81
3^2x(3^2*3-2*3^2)=81
3^2x(9)=3^4
3^2x=3^4/3^2
3^2x=3^2
2x=2
x=1

Like? Yes (7) | No (2)  

abhilasha   10 years AGO

the equation gets fulfilled on keeping x = 1

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Suraj   10 years AGO

put 3^2(x+1)= y

and then solve you wil get y^2-54y-2187=0

factorise and you will get y as 81 and -27

discard -27 as the 3^2(x+1) cannot be -ve. equate
3^2(x+1)= 81 you will get the answer as 1

Like? Yes (2) | No (1)  

IFFAT IRAM   10 years AGO

3^(4x+1) - 2*3^(2x+2) = 81
3*9^2x - 18*9^x = 81
9^2x - 6*9^x = 27
y=9^x
y^2-6y-27=0
(y+3)(y-9)=0
y=9 or -3

9^x=9 or 9^x=-3(not possible)
x=1

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Arigela Naga Vineel   10 years AGO

i got it by substitution

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SREEVIDHYA P P   10 years AGO

3^(4x+1)-2*3^(2x+2)=81
3(3^4x-6*3^2x)=81
3^4x-6*3^2x=27
(3^x)^4-6*(3^x)^2-27=0
Solving this equation we get x=1.
Option is 9

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hareesh   10 years AGO

put x=1

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kaushlendra dutt trivedi   10 years AGO

first put x=1 in the equaction
then i get
LHS=RHS
thus i mark the option no (9)

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harshal agrawal   10 years AGO

taking 3^2x = y
y^2-6y-27=0
i.e. x=1

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vishnuvardhan   10 years AGO

3^(2x)=t
3t^2-18t-81=0
t=9,-3
3^(2x)=9
3^(2x)=3^2
x=1

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AMIT SINGH   10 years AGO

substituting 1 in place of x
we get the required equation,
that is,
LHS=3^(4*1+1)-2*3^(2*1+2)=3^5-2*3^4
=81
RHS=81.
hence value of x=1.

Like? Yes (3) | No (2)  

Sukanya   10 years AGO

substituting x=1
3^5-2*3^4=243-2*81=243-162=81
since x=1 satisfies the given equation, x=1

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Anupam Banerjee   10 years AGO

3^(4x+1)-2*3^(2x+2)=81
or, 3*3^4x-2*3*3*3^2x=81
or, 3^4x-2*3*3^2x=27
(Adding 9 with both side)
or, (3^2x)^2-2*(3^2x)*3+9=27+9
or, (3^2x - 3)^2 = 36
or, 3^2x - 3 = 6
or, 3^2x = 9
or, 2x = 2
or, x=1;

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srilakshmi   10 years AGO

by options
if we replace x with 1(9th option)
3^5-2*3^4 = 243-162 = 81

(or)

3^4x+1 - 2.3^2x+2 = 81
3^4x.3 - 2.3^2x.3^2 = 81(a^m+n = a^m.a^n)
(3^2x)^2*3 - 18*3^2x = 81
let us assume
3^2x = t
3t^2-18t-81 = 0
t^2-6t-27 = 0
by solving this
t = 9
3^2x = 9
9^x = 9^1
so
x=1(as bases equal powers also equal).

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ravi prakash   10 years AGO

3^5=243
2*3^4=162
243-162=81

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Saraswathy   10 years AGO

3^(4x+1) - 2*3^(2x+2) = 81
3^4x * 3^1 - 2* 3^2x * 3^2 = 81
3^2x * 3[3^2 - 2*3] = 3^4
3^2x * 3^2 = 3^4
3^(2x+2) = 3^4
Equate the powers since base is same
2x+2 = 4
x=1
Hence Option (9)

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SIBNATH HALDER   10 years AGO

option 9-1 ans

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manish chauhan   10 years AGO

x=1
3^(4+1)-2*3^(2+2)=81
3^5-2*3^4=81
3^4(3-2)=
81(1)=81 prove

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rajani   10 years AGO

By options on substituting 1 in that equation it is satisfying.
3^5-2(3^4)=243-162=81

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SHEREENA NISHAD   10 years AGO

81= 3^4
3*3^4 - 2* 3^4 =3^4
3^3^4 =3^5 = 3^(4x+1)
4x+1 = 5
x=1

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Deb Das   10 years AGO

3^(4x+1) - 2*3^(2x+2) = 81
3*3^4x-2*9*3^2x=81
3^4x-6*3*3^2x=27
3^4x-9*3^2x+3*3^2x-27=0
3^2x(3^2x-9)+3(3^2x-9)=0
(3^2x-9)(3^2x+3)=0

So,
3^2x=9
3^2x=3^2
2x=2
x=1

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Devendra Marghade   10 years AGO

3^(4x+1) - 2*3^(2x+2) = 81
put 2x=t
3^(2t+1) -2*3^(t+2) = 81
[(3^2t)*3]- [2*(3^t)*3^2] =81
3^t[(3^2)*3 - 2*3^2]=81
3^t(27-18)=81 ,t=2=2x, so x=1

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Jigyasa Kumar   10 years AGO

on putting x = 1 the equation gets satisfied

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Aarush Singh   10 years AGO

x=1 satisfies the equation

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Ramsb   10 years AGO

(3^4x.3)-(2*3^2x*3^2)=81
3(3^4x-6.3^2x)=81
3^2x(3^2-6)=27
3^2x(3)=27
3^2x+1=3^3
2x+1=3
x=1

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Varunraj Reddy   10 years AGO

If x=1 then the equation satisfies.

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