Solve: \(4(2^{x^2}) = 8^{x}\)

Assessment: WAEC SSCE - Further Mathematics - 2015 (Objective) Subject: Further Mathematics

Question 1 Report

Solve: \(4(2^{x^2}) = 8^{x}\)

Answer Details
We can rewrite \(8^x\) as \((2^3)^x = 2^{3x}\). Substituting this into the equation, we have: $$4(2^{x^2}) = 2^{3x}$$ Dividing both sides by \(2^{x^2}\) and simplifying, we get: $$2^{x^2 - 3x + 2} = 0$$ Using the zero-product property of multiplication, we can set the exponent equal to zero: $$x^2 - 3x + 2 = 0$$ Factoring the quadratic, we get: $$(x-1)(x-2) = 0$$ Therefore, the solutions are \(x=1\) and \(x=2\). Hence, the answer is (1, 2).
Read lesson note on Indices And Logarithmic Functions (WAEC)
Read lesson note on Polynomial Functions (WAEC)
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