To solve the equation \(10 \times 3^x + 3 = 60\), let's isolate the term with \(x\).
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Subtract 3 from both sides: \[ 10 \times 3^x = 60 - 3 \] \[ 10 \times 3^x = 57 \]
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Divide both sides by 10: \[ 3^x = \frac{57}{10} \] \[ 3^x = 5.7 \]
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Now, take the logarithm of both sides. We can use natural logarithm (ln) or common logarithm (log). We'll use the natural logarithm: \[ \ln(3^x) = \ln(5.7) \]
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Apply the logarithmic property: \[ x \ln(3) = \ln(5.7) \]
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Now, solve for \(x\): \[ x = \frac{\ln(5.7)}{\ln(3)} \]
Now, let's calculate this using approximate values of logarithms:
- \(\ln(5.7) \approx 1.740466\)
- \(\ln(3) \approx 1.098612\)
Performing the calculation: \[ x \approx \frac{1.740466}{1.098612} \approx 1.585 \]
Now checking the options provided:
- negative 1 point 369
- negative 2 point 387
- negative 1 point 796
- negative 2 point 169
None of these options match the calculated value. Therefore, the solution for \(x\) is not among the given responses. If you are asked to pick an answer, please choose the closest value or verify the equation and context.