if 8^x = y, then what is 2^5x-3 equal to in terms of y?

Given the equation \(8^x = y\), we need to express \(2^{5x-3}\) in terms of \(y\).

First, express \(8^x\) in terms of base 2:
\[ 8 = 2^3 \]
So,
\[ 8^x = (2^3)^x = 2^{3x} \]

This means:
\[ 2^{3x} = y \]

We need to find \(2^{5x-3}\) in terms of \(y\). First, express \(2^{5x-3}\) in a convenient form:
\[ 2^{5x-3} = \frac{2^{5x}}{2^3} \]

Next, relate \(2^{5x}\) to \(y\):
\[ 2^{5x} = (2^{3x})^{\frac{5}{3}} \]
Since \(2^{3x} = y\

Explore how to solve the equation 8^x = y and find 2^(5x-3) in terms of y. This problem involves exponentiation and logarithmic identities, providing a detailed mathematical approach. Suitable for advanced high school students (Grades 10-12).

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