ny_quant | My comment to an entry 'меньше 20%' by avva

Спросил у Microsoft Copilot, который говорят сидит на ChatGPT 4. Solution: 10.8. Ваше решение правильное. Далеко еще ИИ до Эксела.

To solve this, we’ll use logarithms. First, let’s take the natural logarithm (ln) of both sides to remove the variable from the exponent:

[ \ln(7 \times 1.08^t) = \ln(10 \times 1.05^t) ]

Now, we can apply logarithm properties. Using the rule (\ln(a \cdot b) = \ln(a) + \ln(b)), we get:

[ \ln(7) + \ln(1.08^t) = \ln(10) + \ln(1.05^t) ]

Next, we use the property (\ln(a^b) = b \cdot \ln(a)):

[ \ln(7) + t \cdot \ln(1.08) = \ln(10) + t \cdot \ln(1.05) ]

Now, let’s isolate the variable (t):

[ t \cdot \ln(1.08) - t \cdot \ln(1.05) = \ln(10) - \ln(7) ]

Factor out the common factor of (t):

[ t \cdot (\ln(1.08) - \ln(1.05)) = \ln(10) - \ln(7) ]

Finally, solve for (t):

[ t = \frac{\ln(10) - \ln(7)}{\ln(1.08) - \ln(1.05)} ]

Using a calculator, we find that (t \approx 10.8).

Therefore, the approximate value of (t) that satisfies the equation is 10.8.