Given that 1160.26 = x, 1160.1 = y and xz = y4, then the value of z is close to:
1.54
xz = (1160.26)z = 1160.26z, and y4 = (1160.1)4 = 1160.4.
The bases are the same, so the exponents are equal: 0.26z = 0.4.
z = \(\frac{0.4}{0.26} = \frac{20}{13} \approx 1.538\), which is close to 1.54.
Hence, the answer is 1.54.
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