### Home > INT3 > Chapter 7 > Lesson 7.2.5 > Problem7-119

7-119.

Solve for $x, y$, 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.