Given that \(17^{0.3} = x\), \(17^{0.5} = y\) and \(x^z = y^5\), then the value of z is close to:
8.33
Substitute the values of x and y into the equation \(x^z = y^5\).
\((17^{0.3})^z = (17^{0.5})^5\)
Applying the power-of-a-power rule \((a^m)^n = a^{mn}\): \(17^{0.3z} = 17^{2.5}\).
Since the bases are equal, the exponents must be equal: \(0.3z = 2.5\).
\(z = \frac{2.5}{0.3} = \frac{25}{3} \approx 8.33\).
Hence, the value of z is close to 8.33.
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Important Questions from Surds and Indices
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
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The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
