CEMC Fermat, 2013

Algebra Difficulty 1.4 Junior Find the answer Canada

If $512^x = 64^{240}$ , then $x$ equals

Pick one

Solution

We note that $64=2^6$ and $512=2^9$ .

Therefore, the equation $512^x = 64^{240}$ can be rewritten as $(2^9)^x = (2^6)^{240}$ or $2^{9x}=2^{6(240)}$ .

Since the bases in this last equation are equal, then the exponents are equal, so $9x = 6(240)$ or $x = \frac{1440}{9}=160$ .

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