Question

2log^36(2x-7)=log^6(14-x)

Answer 1

А что означает log?пек

Answer 2

I hope this helps you

Answer 3

To solve the equation 2log₃₆(2x-7) = log₆(14-x), we need to express both sides of the equation using the same base.

Let's start by converting the logarithms to a common base. We'll convert them to the base 10 logarithm:

2log₃₆(2x-7) = log₆(14-x) Using the change of base formula, we can rewrite these logarithms:

2(log(2x-7) / log(36)) = log(14-x) / log(6)

Now we can simplify further.

First, let's simplify the right side:

2(log(2x-7) / log(36)) = log(14-x) / log(6) 2(log(2x-7) / log(36)) = log(14-x) / (log(2) + log(3)) 2(log(2x-7) / log(36)) = log(14-x) / log(2) + log(3)

Next, let's simplify the left side:

2(log(2x-7) / log(36)) = 2(log(2x-7) / log(6^2)) 2(log(2x-7) / log(36)) = 2(log(2x-7) / (2 * log(6))) (log(2x-7) / log(36)) = log(2x-7) / log(6)

Since the left and right sides are equal, we can equate the corresponding parts:

log(2x-7) / (2 * log(6)) = log(14-x) / (log(2) + log(3))

To further simplify, let's multiply both sides by (2 * log(6)) and (log(2) + log(3)) to eliminate the denominators:

(log(2x-7) / (2 * log(6))) * (2 * log(6)) * (log(2) + log(3)) = (log(14-x) / (log(2) + log(3))) * (2 * log(6)) * (log(2) + log(3))

The (2 * log(6)) terms cancel out, as well as the (log(2) + log(3)) terms:

log(2x-7) * (log(2) + log(3)) = log(14-x) * (2 * log(6))

Now, we can expand and simplify further:

log(2x-7) * log(2) + log(2x-7) * log(3) = (2 * log(6)) * log(14-x)

Now we can use the properties of logarithms to simplify this equation further. Using the rule logₐ(b) + logₐ(c) = logₐ(bc), we can rewrite the equation as:

log₄₈((2x-7)^log(3)) = log₆((14-x)^(2 * log(6)))

Now that the bases are the same, the arguments inside the logarithms must be equal:

(2x-7)^log(3) = (14-x)^(2 * log(6))

Solving this equation requires further algebraic manipulation and possibly numerical methods. However, it's worth noting that the equation provided is a highly complex equation, and it might not have a simple algebraic solution.