Express variables in terms of base 112

Given $x = 112^{0.17}$ and $y = 112^{0.94}$.

$x = 112^{0.17}, y = 112^{0.94}$

Substitute into the equation

Substitute $x$ and $y$ into $x^z = y^6$: $(112^{0.17})^z = (112^{0.94})^6$.

$112^{0.17 \times z} = 112^{0.94 \times 6}$

Equate the exponents

Since the bases are identical, set the exponents equal: $0.17 \times z = 5.64$.

$z = \frac{5.64}{0.17}$

Final calculation

Divide 5.64 by 0.17 to get $z \approx 33.1764$, which rounds to 33.18.

$z \approx 33.18$