Let * be a binary operation, on the set of all non-zero real numbers, given by a∗b = ab/5 for all a, b ∈R−{0}. Write the value of x given by 2∗(x∗5)=10.

Solve 2*(x*5)=10 for a*b = ab/5

Question:

Let \( * \) be a binary operation on non-zero real numbers defined by:

\[ a * b = \frac{ab}{5} \]

Find \( x \) if:

\[ 2 * (x * 5) = 10 \]

Step 1: Compute inner operation

\[ x * 5 = \frac{x \cdot 5}{5} = x \]

Step 2: Substitute into equation

\[ 2 * x = 10 \]

Step 3: Apply operation definition

\[ 2 * x = \frac{2x}{5} \]

So,

\[ \frac{2x}{5} = 10 \]

Step 4: Solve for \( x \)

\[ 2x = 50 \Rightarrow x = 25 \]

\[ \boxed{25} \]

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