Determine whether x^y•x^z=z^18
is sometimes, always, or never true. Explain.

9514 1404 393

  sometimes true

Step-by-step explanation:

The equation reduces to ...

  x^y·x^z = z^18

  x^(y+z) = z^18

This is not true in general, but is true for specific cases of x, y, and z. For example,

  4^(7+2) = 2^18 . . . . (x, y, z) = (4, 7, 2)

  4^(7+0) ≠ 0^18 . . . . (x, y, z) = (4, 7, 0)

The equation is sometimes true.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: