Question

If (16)^2x+3=(64)^x+3,then find the value of x

Answer 1

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$\textbf{ here's your solution :- }$

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■ ques. = ( 16 )^2x + 3 = ( 64 )^x + 3

Let's solve the question :-

[ 16 ]^2x + 3 = [ 64 ]^x + 3

[ 4 * 4 ]^2x + 3 = [ 4 * 4 * 4 ]^x + 3

[ 4 ]^2 ( 2x + 3 ) = [ 4 ]^3 ( x + 3 )

Here 4 is common on both sides.

So ,

2 ( 2x + 3 ) = 3 ( x + 3 )

4x + 6 = 3x + 9

4x - 3x = 9 - 6

x = 3

Hence , the value of x is 3.}[/tex]

$\textit{Check answer}$

( 16 )^2x + 3 = ( 64 )^x + 3

[ 4 * 4 ]^2x + 3 = [ 4 * 4 * 4 ]^x + 3

[ 4 ]^2 ( 2x + 3 ) = [ 4 ]^3 ( x + 3 )

Again , 4 is common on both sides.

2 ( 2x + 3 ) = 3 ( x + 3 )

4x + 6 = 3x + 9

Put the value of " x " = - 3

4 * ( 3 ) + 6 = 3 * ( 3 ) + 9

12 + 6 = 9 + 9

18 = 18

$\textbf{Hence proved}$

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Answer 2

Answer:

Given, (16)2x+3=(64)x+3

We can write 16 as 24 and 64=26

So, (24)2x+3=(26)x+3

(2)8x+12=(2)6x+18  

So, 8x+12=6x+18

 8x−6x=18−12

 2x=6

 x=3

We have to find out the value of 42x−2

Keep the value of x 

= 42×3−2

= 46−2

= 44

= 256

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