Question

What is the solution to the equation 49x=sqrt 7^(2x+6)

Answer 1

49x or 49^x ?

Answer 2

49^x ,sorry

Answer 3

Notice first then that because 49 = 7^2, that 49^x = 7^(2x).

Answer 4

yes? Now square both sides:
\[ 7^{4x} = 7^{2x+6} \]
making sense?

Answer 5

sort of

Answer 6

So first, happy with 49^x = 7^2x ?

Answer 7

yes i understand that part

Answer 8

\[ 49^x = (7^2)^x = 7^{2x} \]
Now that is equal to
\[ \sqrt{7^{2x+6}} = (7^{2x+6})^{1/2} \]

Answer 9

okay

Answer 10

and that is equal to
\[ 7^{(2x+6)/2} = 7^{x+3} \]

Answer 11

Hence the original equation
\[ 49^x = 7^{2x+6} \] implies
\[ 7^{2x} = 7^{x+3} \]
because
\[ 49^x = 7^{2x} \]
and
\[ \sqrt{7^{2x+6}} = 7^{x+3} \]

Answer 12

okay

Answer 13

the original equation has a square root I dropped.

Answer 14

So now we have
\[ 7^{2x} = 7^{x+3} \]
what does that imply?

Answer 15

umm, idk

Answer 16

if \[ 7^a = 7^b \]
what can you say about a and b?

Answer 17

they are equal

Answer 18

Yes, a = b.

Hence if
\[ 7^{2x} = 7^{x+3} \]
what can you say.

Answer 19

they are equal also

Answer 20

what's equal? make it explicit; write down the equation.

Answer 21

\[ 7^a = 7^b \ \implies \ a = b \]
hence
\[ 7^{2x} = 7^{x+3} \ \implies \ ...what? \]

Answer 22

still there?

Answer 23

i need help on this to.
so your saying 2x = x +3??

Answer 24

Yes

Answer 25

This helped me so much! Thanks for taking the time to answer this for her!