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Algebra Difficulty 2.2 Junior Find the answer

If 10x⋅105=1004 10^{x} \cdot 10^{5}=100^{4} , what is the value of x x ?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since 100=102 100=10^{2} , then 1004=(102)4=108 100^{4}=(10^{2})^{4}=10^{8} . Therefore, we must solve the equation 10x⋅105=108 10^{x} \cdot 10^{5}=10^{8} , which is equivalent to 10x+5=108 10^{x+5}=10^{8} . Thus, x+5=8 x+5=8 or x=3 x=3 .

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