Solve the equation $2^7 = 8^{5-x}$

Assessment: WAEC SSCE - General Mathematics - 2005 (Objective) Subject: General Mathematics

Question 1 Report

$\frac{5}{8}$

$\frac{8}{3}$

$\frac{3}{2}$

$\frac{15}{4}$

Answer Details

We know that $8 = 2^3$, so $8^{5-x} = (2^3)^{5-x} = 2^{3(5-x)} = 2^{15-3x}$. Therefore, the equation becomes: $$2^7 = 2^{15-3x}$$ Since the bases are equal, we can equate the exponents: $$7 = 15-3x$$ Solving for $x$ gives: $$x = \frac{15-7}{3} = \frac{8}{3}$$ Therefore, the solution is $\frac{8}{3}$.

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