Question
If 10logx=1/10³², what is the value of x?(1 point)
Responses
32
−32
10³²
10−³²
Responses
32
−32
10³²
10−³²
Answers
Answered by
GPT-4o mini
To solve the equation \( 10 \log x = \frac{1}{10^{32}} \), we can first isolate \( \log x \):
\[
\log x = \frac{1}{10 \cdot 10^{32}} = \frac{1}{10^{33}}
\]
Next, we can express \( x \) in terms of base 10 using the property of logarithms:
\[
x = 10^{\log x} = 10^{\frac{1}{10^{33}}}
\]
Thus, the value of \( x \) is:
\[
x = 10^{\frac{1}{10^{33}}}
\]
Looking at the provided responses:
- \( 32 \)
- \( -32 \)
- \( 10^{32} \)
- \( 10^{-32} \)
None of these responses exactly match \( 10^{\frac{1}{10^{33}}} \). However, if we consider the expression itself, it appears that the answer choices given might have an error since none of them directly relate to \( 10^{\frac{1}{10^{33}}} \).
The expected final value for \( x \) is \( 10^{\frac{1}{10^{33}}} \). If you are looking for the closest numerical representation in the context of orders of magnitude based on logarithmic responses, the options do not fit.
Please review the options provided. If they were expected to be in logarithmic form, the correct evaluation would be \( 10^{\frac{1}{10^{33}}} \) which is not in the list. If there’s a misunderstanding or a typo in the answers, you might want to double-check that as well.
\[
\log x = \frac{1}{10 \cdot 10^{32}} = \frac{1}{10^{33}}
\]
Next, we can express \( x \) in terms of base 10 using the property of logarithms:
\[
x = 10^{\log x} = 10^{\frac{1}{10^{33}}}
\]
Thus, the value of \( x \) is:
\[
x = 10^{\frac{1}{10^{33}}}
\]
Looking at the provided responses:
- \( 32 \)
- \( -32 \)
- \( 10^{32} \)
- \( 10^{-32} \)
None of these responses exactly match \( 10^{\frac{1}{10^{33}}} \). However, if we consider the expression itself, it appears that the answer choices given might have an error since none of them directly relate to \( 10^{\frac{1}{10^{33}}} \).
The expected final value for \( x \) is \( 10^{\frac{1}{10^{33}}} \). If you are looking for the closest numerical representation in the context of orders of magnitude based on logarithmic responses, the options do not fit.
Please review the options provided. If they were expected to be in logarithmic form, the correct evaluation would be \( 10^{\frac{1}{10^{33}}} \) which is not in the list. If there’s a misunderstanding or a typo in the answers, you might want to double-check that as well.