Question

2(3)^x = 3^x + 1?

Answer 1

\(\large 2*3^x=3^{x+1}\)? what are we doing? solving for x?

Answer 2

yes @bibby

Answer 3

divide both sides by 3^x

Answer 4

are you sure the problem is not
\[ 2\cdot 3^x = 3^x + 1 \]

Answer 5

i figured it was a log problem

Answer 6

there is no solution the other way

Answer 7

oh yeah, my bad

Answer 8

2=3

Answer 9

@phi yes sorry! i just looked and you're correct, i was mistaken

Answer 10

yes and 2=3 means no solution (most experts agree that 2 is not equal to 3)

Answer 11

but to solve, you can still use bibby's advice
or you can "combine like terms"

Answer 12

ohhhh! i get it. so the answer is x = no solution?

Answer 13

if you temporarily rename 3^x as y, you have
2 y = y + 1

Answer 14

now solve for y. what do you get ?

Answer 15

***ohhhh! i get it. so the answer is x = no solution?***
only if the problem is
\[ 2\cdot 3^x = 3^{x+1} \]

Answer 16

to solve
\[ 2\cdot 3^x = 3^x + 1 \]
temporarily rename 3^x as y
\[ 2y= y+1 \]
solve for y by adding -y to both sides.
can you do that ?