SOLUTION: {{{ 4 raised to the power of 3x = 7 raised to the power of (x+1) }}} meaning... {{{ 4 ^ (3x) = 7 ^ (x+1) }}} Thank you!! :)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: {{{ 4 raised to the power of 3x = 7 raised to the power of (x+1) }}} meaning... {{{ 4 ^ (3x) = 7 ^ (x+1) }}} Thank you!! :)      Log On


   

Question 1115212: +4+raised+to+the+power+of+3x+=+7+raised+to+the+power+of+%28x%2B1%29+
meaning...
+4+%5E+%283x%29+=+7+%5E+%28x%2B1%29+
Thank you!! :)
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+4%5E%283x%29+=+7%5E%28x%2B1%29+
3x*log(4) = (x+1)*log(7)
x*log(64) = x*log(7) + log(7)
x*log(64) - x*log(7) = log(7)
x*(log(64) - log(7)) = log(7)
x = log(7)/(log(64/7)
x =~ 0.87932

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
I assume x is over the real numbers
:
4^(3x) = 7^(x+1)
:
take the natural logarithms of both sides of = and use identity log a^b = blog a
:
3xln 4 = ln 7(x+1)
:
Note 3xln 4 = 6xln 2
:
6xln 2 = (x+1)ln 7
:
6xln 2 = xln 7 + ln 7
:
(6ln 2 - ln 7)x = ln 7
:
x = ln 7 / (6ln 2 - ln 7) = ln 7 / (ln 64 / ln 7) = 0.9105
: