Question

solve : 3^4x+7 = 4^2x+3.....solve for x

Answer 1

this one?

Answer 2

are those all in the exponent? (..) would help it they are

Answer 3

3^(4x+7) = 4^(2x+3)

log3 (3^(4x+7) = 4^(2x+3))

4x+7 = (2x+3) log3(4)


4x+7
----- = log3(4)
2x+3

hmmm....

Answer 4

what does the log do?

Answer 5

\[b^{n+m}=b^n*b^m\]might help

3^(4x+7) = 4^(2x+3)

3^(4x) * 3^7 = 4^(2x)* 4^3

3^(4x) * 3^7 = 4^(2x)* 4^3

3^(4x) = 4^(2x) * N

3^(4x)
------ = N
4^(2x)

log helps to undo exponent bases

Answer 6

ok thanks a lot!!! you sound like you know a lot about this stuff...im in precalc and these are things we havent relee learned yet

Answer 7

log4 (3^(4x) = 4^(2x) * N)

4x log4(3) = 2x + log4(N)

4x log4(3) - 2x= log4(N)

x(4 log4(3) - 2)= log4(N)


log4(N)
x= --------------
log4(3^4) - 2


log4(4^3/3^7)
x= --------------
log4(3^4) - 2



3-7 log4(3)
x= -------------
4 log4(3) - 2

maybe, might wanna chk with the wolf on that tho

Answer 8

http://www.wolframalpha.com/input/?i=y%3D3%5E%284x%2B7%29-4%5E%282x%2B3%29%3B+x%3D%283-7+log%283%29%2Flog%284%29%29%2F%284log%283%29%2Flog%284%29-2%29

its says its 0 :)