Question

3log²₆x-4log₆36x+1=0

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation 3log₂₆x - 4log₆36x + 1 = 0, we'll use some logarithmic properties to simplify it step by step:

1. Use the properties of logarithms to rewrite log₆36x: log₆36x = log₆36 + log₆x Since 36 is 6², we have: log₆36 = log₆(6²) = 2log₆6

   So, log₆36x = 2log₆6 + log₆x

2. Substitute this back into the original equation: 3log₂₆x - 4(2log₆6 + log₆x) + 1 = 0

3. Distribute the -4 to both terms inside the parentheses: 3log₂₆x - 8log₆6 - 4log₆x + 1 = 0

4. Combine the like terms (log₆x terms): (3 - 4)log₆x = -8log₆6 - 1 -log₆x = -8log₆6 - 1

5. Divide both sides by -1 to isolate log₆x: log₆x = 8log₆6 + 1

6. Now, we'll convert the equation into exponential form. Remember that in exponential form, if you have logₐb = c, then it can be written as a^c = b.

   So, in this case: x = 6^(8log₆6 + 1)

7. Use the properties of logarithms to simplify further: x = 6^(8log₆6) * 6¹

8. Since 6 is the base of the logarithm, 6^(log₆6) = 6, so we have: x = 6^8 * 6

9. Calculate 6^8: x = 1679616 * 6

10. Multiply to find the final result: x = 10077696

So, the solution to the equation 3log₂₆x - 4log₆36x + 1 = 0 is x = 10077696.