CEMC Fermat, 2014

Algebra Difficulty 1.4 Junior Find the answer Canada

If $10^x \cdot 10^5 = 100^4$ , what is the value of $x$ ?

Pick one

Solution

Since $100=10^2$ , then $100^4 = (10^2)^4 = 10^8$ .

Therefore, we must solve the equation $10^x \cdot 10^5 = 10^8$ , which is equivalent to $10^{x+5}=10^8$ .

Thus, $x+5=8$ or $x=3$ .

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