Question

Решить уравнение log4(2x-5)=-1

Answer 1

$\log_4(2x-5)=-1 \\2x-5\ \textgreater \ 0 \\2x\ \textgreater \ 5 \\x\ \textgreater \ 2,5 \\x\in (2,5;+\infty) \\2x-5=4^{-1} \\2x-5= \frac{1}{4} \\2x=5+0,25 \\2x=5,25 \\x=2,625\in (2,5;+\infty)$
Ответ: x=2,625

Answer 2

To solve the equation log₄(2x - 5) = -1, we need to understand that the logarithm function with base 'a' (logₐ) is the inverse of the exponentiation function with base 'a'. Therefore, logₐ(b) = c is equivalent to a^c = b.

In this case, we have log₄(2x - 5) = -1, which means 4^(-1) = 2x - 5.

Let's solve for 'x':

4^(-1) = 1/4

So, the equation becomes:

1/4 = 2x - 5

Now, we isolate 'x' by adding 5 to both sides:

1/4 + 5 = 2x

Next, simplify the left side:

20/4 = 2x

Now, divide both sides by 2:

10/4 = x

Finally, simplify the fraction:

x = 5/2

So, the solution to the equation is x = 5/2 or x = 2.5.