Question 81
Consider the equations
$$
3^{2x+3} - 2^{x+2} = 2^{x+5} - 9^{x+1}
$$
and
$$
a \cdot 5^{2x} + |a-1| 5^{x} = 1
$$
where $a$ is a real number.
a) Solve the equation (1).
b) Find the values of $a$ such that the equations (1) and (2) are equivalent.
$$
3^{2x+3} - 2^{x+2} = 2^{x+5} - 9^{x+1}
$$
and
$$
a \cdot 5^{2x} + |a-1| 5^{x} = 1
$$
where $a$ is a real number.
a) Solve the equation (1).
b) Find the values of $a$ such that the equations (1) and (2) are equivalent.