Initial Equations Analysis
We are given the following information:
- $7^{0.07} = x$
- $7^{0.07} = y$
- $x^z = y^3$
The goal is to determine the value of $z$.
Deriving the Value of z
From the first two equations, it's clear that both $x$ and $y$ are equal to the same value, $7^{0.07}$. Therefore, we can conclude that $x = y$.
Now, we substitute $x = y$ into the third equation, $x^z = y^3$:
$x^z = x^3$
Since $x = 7^{0.07}$, the base $x$ is a positive number not equal to 1. For the equation $x^z = x^3$ to hold true, the exponents must be equal.
$z = 3$
Conclusion
The exact value of $z$ is 3. This matches Option 3 directly.
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Important Questions from Surds and Indices
Find the cube root of 78402752
Find the value of :
[(3 × 3 × 3 × 3 × 3 × 3) 6 ÷ (3 × 3 × 3 × 3) 7 × 3 4]
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 = ?
