Answer:
D. 4
Explanation:
Without actually solving the equation, recall that for
, there are two cases:
![\begin{cases}a=b, \\a=-b\end{cases}](https://img.qammunity.org/qa-images/2022/formulas/mathematics/high-school/yxd1ehbqjx1aqe8nh515oo.png)
In the given equation
, there are two pairs of absolute value symbols.
Since each has two cases, there must be a total of
different equations created.
All four cases are:
![\begin{cases}(x-2)^(10x^2-1)=(x-2)^(3x),\\(-x+2)^(10x^2-1)=(x-2)^(3x),\\(x-2)^(10x^2-1)=(-x+2)^(3x),\\(-x+2)^(10x^2-1)=(-x+2)^(3x)\end{cases}](https://img.qammunity.org/qa-images/2022/formulas/mathematics/high-school/mgz1s8067goyprky4yendx.png)
Exponents differ, hence clearly there are four possible solutions to this equation.
You can solve for all four values of
by taking the log of both sides and using a bit of algebra to verify you have four solutions.