If \(2^{x} = 8^{\,y+1}\) and \(9^{\,y} = 3^{\,x-9}\), then the value of \(x\) is:

Question

If \( 5\sqrt{5} \times 5^3 \div 5^{-3/2} = 5^a \), then the value of \( a \) is:

Answer 1

Step 1: \(2^x = 2^{3(y+1)} \Rightarrow x = 3y + 3\).
Step 2: \(3^{2y} = 3^{x-9} \Rightarrow 2y = x - 9\). Substitute \(x=3y+3\): \(2y = 3y - 6 \Rightarrow y = 6\).
Step 3: So \(x = 3(6)+3 = 21\).

Quick Tip: Rewrite both sides with the same base, then equate the exponents.

If \(2^{x} = 8^{\,y+1}\) and \(9^{\,y} = 3^{\,x-9}\), then the value of \(x\) is:

The Correct Option is A

Solution and Explanation

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