<PRE><B>Question 1115212</B>
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
:
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