Question

Solve for x by rewriting both sides as powers of the same base:
3^x= (9^(x-1)) 27^(1-3x)

Answer 1

there are three different bases in this equation... 3, 9 and 27... all three have their own powers.. but that really doesnt affect the processin this case... you want to change 3 9 and 27 into the same base.. meaning the same number raised to whatever power will give you the original number.. ex. 9 becomes 3^2... 27 becomes 3^3..\[3^{x} = 3^{2(x-1)}\times3^{3(1-3x)}\]

Answer 2

then you can simplify the powers 2(x-1) and 3(1-3x)

Answer 3

I get that but don't know how to solve this particular type of problem

Answer 4

so its 2x-2 and 3-9x

Answer 5

then join like terms -7x -1?

Answer 6

yeah, those are the powers of the final answer

Answer 7

if the problem just asks to change the numbers to the same base, then that answer is enough

Answer 8

it says solve for x though

Answer 9

oh.. woops didn't see that part

Answer 10

thats where Im having trouble

Answer 11

its cool

Answer 12

once you get the same base, take the \[\log_{3} \] of both sides, which will leave you with x = 2x-2 + 3 - 9x

Answer 13

remember when you multiply bases, you add the powers.. so when you take the log of both sides the base is removed and the powers become added

Answer 14

ok, so x=-7x + 1
8x=1
x=1/8?

Answer 15

is that right?

Answer 16

yeah, that's right

Answer 17

great, thanks man

Answer 18

no problem, glad i could help

Answer 19

keep posting, i'll keep answering for the next hour or so

Answer 20

okay will do if I get stuck with another problem