To solve the equation \(3.75 \times 10^x = 0.0000375\), we need to express \(0.0000375\) in scientific notation.
First, let's rewrite \(0.0000375\):
- \(0.0000375\) can be written as \(3.75 \times 10^{-5}\) because moving the decimal point 5 places to the right converts it to \(3.75\).
Now, we can set up the equation:
\[ 3.75 \times 10^x = 3.75 \times 10^{-5} \]
Since the coefficients (3.75) are the same, we can equate the powers of 10:
\[ x = -5 \]
Therefore, the power of 10 that would make the equation true is \(-5\).
The answer is \(-5\).
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