Question
If 10logx=1/10^7 , what is the value of x?(1 point) Responses −7 negative 7 7 7 107 10 superscript 7 baseline 10−7
Answers
Answered by
GPT-4o mini
To solve the equation \( 10 \log x = \frac{1}{10^7} \), we first simplify it.
1. Divide both sides by 10:
\[
\log x = \frac{1}{10^8}
\]
2. Convert the logarithmic equation to exponential form:
\[
x = 10^{\frac{1}{10^8}}
\]
Thus, the solution for \( x \) is:
\[
x = 10^{\frac{1}{10^8}}
\]
Since \( \frac{1}{10^8} \) is a small positive number, \( 10^{\frac{1}{10^8}} \) is slightly greater than 1. The value of \( x \) is therefore approximately \( 1.0000000023 \), but that precise value isn't listed in your answer options.
From the answer choices you provided:
- \( -7 \)
- \( 7 \)
- \( 10^7 \)
- \( 10^{-7} \)
The most appropriate conclusion about relative sizes does not seem to match the options directly.
However, if we consider approximations for the logarithmic relationship \( 10 \log x = -7 \), we get:
\[
\log x \approx -0.7
\]
This gives us:
\[
x \approx 10^{-0.7} \approx 0.2
\]
Clearly, if it refers back to a simpler form without confusion and given context, the closest we could guess from the available options would lean towards choosing \( 10^{-7} \), since \( \log 10^{-7} = -7 \).
Final answer from choices provided: **\( 10^{-7} \)**.
1. Divide both sides by 10:
\[
\log x = \frac{1}{10^8}
\]
2. Convert the logarithmic equation to exponential form:
\[
x = 10^{\frac{1}{10^8}}
\]
Thus, the solution for \( x \) is:
\[
x = 10^{\frac{1}{10^8}}
\]
Since \( \frac{1}{10^8} \) is a small positive number, \( 10^{\frac{1}{10^8}} \) is slightly greater than 1. The value of \( x \) is therefore approximately \( 1.0000000023 \), but that precise value isn't listed in your answer options.
From the answer choices you provided:
- \( -7 \)
- \( 7 \)
- \( 10^7 \)
- \( 10^{-7} \)
The most appropriate conclusion about relative sizes does not seem to match the options directly.
However, if we consider approximations for the logarithmic relationship \( 10 \log x = -7 \), we get:
\[
\log x \approx -0.7
\]
This gives us:
\[
x \approx 10^{-0.7} \approx 0.2
\]
Clearly, if it refers back to a simpler form without confusion and given context, the closest we could guess from the available options would lean towards choosing \( 10^{-7} \), since \( \log 10^{-7} = -7 \).
Final answer from choices provided: **\( 10^{-7} \)**.