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0.00000000013284 is equal to 13284(10-x). What is the value of x ?

 Aug 26, 2017

To solve the equation \(0.00000000013284=13284\times10^{-x}\), we must realize that we are trying to get the same base. First, convert \(0.00000000013284\) into a scientific form. 


To do this, move the decimal point of \(0.00000000013284\) such that the decimal point moves in front of the first nonzero digit of the number. The number of times one moves is what the 10 will be raised to. Knowing this, \(0.00000000013284=1.3284\times10^{-10}\). We have now changed the equation to the following:



Now, let's continue moving that decimal of 1.3284 to the right. We'll move it 4 decimal places. This means that \(1.3284\times10^{-10}=13284\times10^{-14}\). Oh look! we have the same base now. Let's solve for x:


\(13284\times10^{-14}=13284\times10^{-x}\) Divide by 13284 on both sides.
\(10^{-14}=10^{-x}\) Our goal is to make the exponents the same. With this equation, the following is implied.
\(-14=-x\) Divide by -1 on both sides.


And there you go! 

 Aug 26, 2017

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