Question

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

Answer 1

2x+1=14
2x=13
x=13/2
можно сбросить log2

Answer 2

To solve the equation log2(2x + 1) = log2(13) + 1, we can use the properties of logarithms.

First, let's simplify the equation by applying the property that states loga(b) = c is equivalent to a^c = b:

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

Next, we can simplify the right side of the equation:

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

Since 2^(log2(13)) equals 13 (since the logarithm base and exponent cancel each other out), we can substitute it into the equation:

2x + 1 = 2 * 13

Simplifying further:

2x + 1 = 26

Now, let's solve for 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 or x = 12.5.