Question

3^x=9^x+1 how to solve

Answer 1

\[3^x=9^{x+1}\]?

Answer 2

Is it??

Answer 3

yes

Answer 4

can you show formulas or/and your work please

Answer 5

You can write it as:

\[3^x = (3^2)^{x+1}\]

\[\large 3^x = 3^{2x+2}\]

Now exponents must be equal..

So equate the exponents and find x from there..

Answer 6

so do you cancel the threes and solve for x when you have ^x=2x+2

Answer 7

See, the two equations are equal..

Their base(3) is also the same..

If they are equal then their exponents must be equal..

So we here equate the exponents..

Answer 8

In general:

\[\huge x^a = x^b \implies \color{green}{a = b}\]

Answer 9

I'm still confused I'm not just looking for the answer but I'm better at analyzing the work what values would a and b be

Answer 10

Here a = x and b = 2x + 2

Answer 11

so x=2x+2

Answer 12

so i subtract from from both sides then subtract x so i get x=-2

Answer 13

Yes you are right..

Answer 14

See first his reply..

He replied yes to Turning test..

Answer 15

oh... so this problem is easier than what i have then....

Answer 16

Ha ha ha..

Yes it is..