Question
Solve the exponential equation. 6−3+5x= 64x − 10 (1 point) Responses x =−7 x =−7 x =−13 x =−13 x =−9 x =−9 x =−3
Answers
GPT-4o mini
To solve the equation \(6^{-3 + 5x} = 64x - 10\), we can start simplifying and analyzing both sides.
First, rearranging the left-hand side:
1. \(6^{-3 + 5x} = 64x - 10\)
Next, let's solve or find values for \(x\). The exponential function tends to grow fast, while the linear function on the right might not accommodate multiple solutions easily.
You can evaluate each response by substituting the value of \(x\):
1. **For \(x = -7\)**:
\[
6^{-3 + 5(-7)} = 6^{-3 - 35} = 6^{-38}
\]
\[
64(-7) - 10 = -448 - 10 = -458
\]
Left side = \(6^{-38}\), Right side = \(-458\) (Not equal)
2. **For \(x = -13\)**:
\[
6^{-3 + 5(-13)} = 6^{-3 - 65} = 6^{-68}
\]
\[
64(-13) - 10 = -832 - 10 = -842
\]
Left side = \(6^{-68}\), Right side = \(-842\) (Not equal)
3. **For \(x = -9\)**:
\[
6^{-3 + 5(-9)} = 6^{-3 - 45} = 6^{-48}
\]
\[
64(-9) - 10 = -576 - 10 = -586
\]
Left side = \(6^{-48}\), Right side = \(-586\) (Not equal)
4. **For \(x = -3\)**:
\[
6^{-3 + 5(-3)} = 6^{-3 - 15} = 6^{-18}
\]
\[
64(-3) - 10 = -192 - 10 = -202
\]
Left side = \(6^{-18}\), Right side = \(-202\) (Not equal)
Since substituting all possible values results in mismatches, we can conclude that likely, none of these values solve the original equation.
Please double-check each computation and ensure the equation is correct, as none of the proposed options satisfy the original equation.
If needed, we can explore graphing or numerical methods to approximate solutions. If you need further assistance, please provide extra context or confirm the original equation.
First, rearranging the left-hand side:
1. \(6^{-3 + 5x} = 64x - 10\)
Next, let's solve or find values for \(x\). The exponential function tends to grow fast, while the linear function on the right might not accommodate multiple solutions easily.
You can evaluate each response by substituting the value of \(x\):
1. **For \(x = -7\)**:
\[
6^{-3 + 5(-7)} = 6^{-3 - 35} = 6^{-38}
\]
\[
64(-7) - 10 = -448 - 10 = -458
\]
Left side = \(6^{-38}\), Right side = \(-458\) (Not equal)
2. **For \(x = -13\)**:
\[
6^{-3 + 5(-13)} = 6^{-3 - 65} = 6^{-68}
\]
\[
64(-13) - 10 = -832 - 10 = -842
\]
Left side = \(6^{-68}\), Right side = \(-842\) (Not equal)
3. **For \(x = -9\)**:
\[
6^{-3 + 5(-9)} = 6^{-3 - 45} = 6^{-48}
\]
\[
64(-9) - 10 = -576 - 10 = -586
\]
Left side = \(6^{-48}\), Right side = \(-586\) (Not equal)
4. **For \(x = -3\)**:
\[
6^{-3 + 5(-3)} = 6^{-3 - 15} = 6^{-18}
\]
\[
64(-3) - 10 = -192 - 10 = -202
\]
Left side = \(6^{-18}\), Right side = \(-202\) (Not equal)
Since substituting all possible values results in mismatches, we can conclude that likely, none of these values solve the original equation.
Please double-check each computation and ensure the equation is correct, as none of the proposed options satisfy the original equation.
If needed, we can explore graphing or numerical methods to approximate solutions. If you need further assistance, please provide extra context or confirm the original equation.