### Home > CCA2 > Chapter 6 > Lesson 6.1.3 > Problem6-43

6-43.

Solve for $x,y,\ \text{and}\ z$: $(2^x)(3^y)(5^z)=(2^3)(3^{x−2})(5^{2x−3y})$.

Make a system of equations using the exponents.

$x=3\\y=x−2\\z=2x−3y$

The system of equations gives you the value of $x$. Substitute the value of $x$ into the second and third equations.
From there, solve as if there were only two equations.