Question 46234
these types of questions look really hard but at very simple (usually :-) ).


The thing to spot is that the 2 base numbers, here 9 and 27 are both powers of 3. We will convert the numbers to 3 and then we will have "3 to the power of whatever" equals "3 to the power of something else". So, the 2 powers must be the same thing.


{{{ 9^(2x + 1) = 27^x }}}
{{{ (3^2)^(2x + 1) = (3^3)^x }}}
{{{ 3^(2(2x+1)) = 3^(3x) }}}


So now we can say that
{{{ 2(2x+1) = 3x }}}
{{{ 4x+2 = 3x }}}
{{{ x+2 = 0 }}}
{{{ x = -2 }}}


CHECK:
{{{ 9^(2(-2) + 1) = 27^(-2) }}}
{{{ 9^(-4+1) = 27^(-2) }}}
{{{ 9^(-3) = 27^(-2) }}}
{{{ 1/9^(3) = 1/27^(2) }}}
{{{ 1/(3^2)^(3) = 1/(3^3)^(2) }}}
{{{ 1/(3^6) = 1/(3^6) }}}


so we are correct.


jon