Question
3.) How do you find the missing exponent? (1 point)
Answers
Answer
the equation is b^350/b ? = b^113. What is the missing number
Answered by
GPT-4o mini
To find a missing exponent in an equation or expression, you typically want to isolate the variable with the exponent. Here’s a step-by-step method:
1. **Set up the equation**: Start with the given equation that has a missing exponent. For example, if you have \( a^x = b \), where \( x \) is the missing exponent.
2. **Apply logarithms**: If the missing exponent is part of a power equation, you can take the logarithm of both sides to help isolate the exponent. For instance:
\[
\log(a^x) = \log(b)
\]
3. **Use the power rule of logarithms**: This rule states that \( \log(a^x) = x \cdot \log(a) \).
So, applying the rule gives:
\[
x \cdot \log(a) = \log(b)
\]
4. **Solve for the exponent**: To solve for \( x \), divide both sides by \( \log(a) \):
\[
x = \frac{\log(b)}{\log(a)}
\]
5. **Calculate**: Plug in the values for \( a \) and \( b \) to find the value of the exponent \( x \).
This method works for finding missing exponents in various contexts, such as growth/decay problems, exponential equations, and logarithmic equations. If you have a specific equation in mind, feel free to share it for a more detailed explanation!
1. **Set up the equation**: Start with the given equation that has a missing exponent. For example, if you have \( a^x = b \), where \( x \) is the missing exponent.
2. **Apply logarithms**: If the missing exponent is part of a power equation, you can take the logarithm of both sides to help isolate the exponent. For instance:
\[
\log(a^x) = \log(b)
\]
3. **Use the power rule of logarithms**: This rule states that \( \log(a^x) = x \cdot \log(a) \).
So, applying the rule gives:
\[
x \cdot \log(a) = \log(b)
\]
4. **Solve for the exponent**: To solve for \( x \), divide both sides by \( \log(a) \):
\[
x = \frac{\log(b)}{\log(a)}
\]
5. **Calculate**: Plug in the values for \( a \) and \( b \) to find the value of the exponent \( x \).
This method works for finding missing exponents in various contexts, such as growth/decay problems, exponential equations, and logarithmic equations. If you have a specific equation in mind, feel free to share it for a more detailed explanation!
Answered by
GPT-4o mini
To solve the equation \( \frac{b^{350}}{b} = b^{113} \), we can follow these steps:
1. **Simplify the left side**: Use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).
\[
\frac{b^{350}}{b} = b^{350 - 1} = b^{349}
\]
Thus, the equation becomes:
\[
b^{349} = b^{113}
\]
2. **Set the exponents equal**: Since the bases are the same (both are \( b \)), we can set the exponents equal to each other:
\[
349 = 113
\]
3. **Find the missing exponent**: However, upon simplification we see that this is not correct since clearly \( 349 \neq 113\).
This implies we need another context or check to see what we want from "the missing number." If you were looking for how to solve it, we assume a scenario where the exponent might be unknown, we could reformulate the statement differently or provide a clearer equation context.
As it stands, we found the operations validly. If a different format of the equation or clarification about "missing number" can be offered, please let me know!
1. **Simplify the left side**: Use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).
\[
\frac{b^{350}}{b} = b^{350 - 1} = b^{349}
\]
Thus, the equation becomes:
\[
b^{349} = b^{113}
\]
2. **Set the exponents equal**: Since the bases are the same (both are \( b \)), we can set the exponents equal to each other:
\[
349 = 113
\]
3. **Find the missing exponent**: However, upon simplification we see that this is not correct since clearly \( 349 \neq 113\).
This implies we need another context or check to see what we want from "the missing number." If you were looking for how to solve it, we assume a scenario where the exponent might be unknown, we could reformulate the statement differently or provide a clearer equation context.
As it stands, we found the operations validly. If a different format of the equation or clarification about "missing number" can be offered, please let me know!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.