Question

Log2(2x+1)=log2(13)+1

Answer 1

Логарифмируем 1, это  $log_{2}2$. Сложение логарифмов с одинаковым основанием есть произведение их под логарифмических выражений, т.е. 
$log_{2}13+log_{2}2=log_{2}26$, тогда
$log_{2}(2x+1)=log_{2}26$
$2x+1=26$
$2x=25$
$x=12,5$
Ответ:12,5

Answer 2

To solve the equation log2(2x+1) = log2(13) + 1, we can use the properties of logarithms. In this case, we can start by converting the equation into exponential form.

The logarithmic equation log2(2x+1) = log2(13) + 1 can be rewritten as:

2x+1 = 2^(log2(13) + 1)

Since 2^(log2(13) + 1) can be simplified as 2 * 2^(log2(13)), and 2^(log2(13)) is equal to 13, we have:

2x+1 = 2 * 13

Simplifying further:

2x+1 = 26

Now, we can solve for x by isolating the term with x:

2x = 26 - 1

2x = 25

Dividing both sides by 2:

x = 25/2

Therefore, the solution to the equation log2(2x+1) = log2(13) + 1 is x = 25/2.