Question 35645
{{{8^(3x+4) = 3^x}}}


First, take the ln of each side of the equation:
{{{ ln  8^(3x+4) = ln  3^x}}}


By the third law of exponents, "bring the exponents down" to become coefficients:

{{{(3x+4) * ln 8 = x* ln 3}}}


Distributive property:

{{{3x * ln 8 + 4 * ln 8 = x * ln 3}}}


Get all the x terms on one side and the non-x terms on the other side.  You might want to subtract {{{ 3x ln 8}}} from each side:

{{{ 4* ln 8 = x * ln 3 - 3x* ln 8}}}


Factor out the x on the left side in order to get the x in one place, so you can solve for x.
{{{4* ln 8 = x(ln 3 - 3 * ln 8) }}}


Divide both sides by {{{ (ln 3 - 3 * ln 8) }}}


{{{x = (4* ln 8)/( ln3 - 3 * ln 8)}}}


Calculate with a calculator:  x =  -1.618 approximately.  


Thank you so much for this problem!!  I could put it on my final exam for College Algebra next week!!


R^2 at SCC