Question

Log4(x+1)-2=log 4(3-x)

Answer 1

Ответ:

решение представлено на фото

Answer 2

To solve the equation log4(x + 1) - 2 = log4(3 - x), we can start by combining the logarithms on the right side using the logarithmic identity:

log4(a) - log4(b) = log4(a/b)

Applying this identity, we have:

log4(x + 1) - log4(3 - x) = 2

Using the logarithmic identity, we can rewrite the equation as:

log4[(x + 1) / (3 - x)] = 2

To eliminate the logarithm, we can rewrite the equation in exponential form:

4^2 = (x + 1) / (3 - x)

Simplifying the left side:

16 = (x + 1) / (3 - x)

Now we can cross-multiply:

16(3 - x) = x + 1

48 - 16x = x + 1

Combine like terms:

48 = 17x + 1

Subtracting 1 from both sides:

47 = 17x

Dividing both sides by 17:

x = 47 / 17

Therefore, the solution to the equation log4(x + 1) - 2 = log4(3 - x) is:

x = 47 / 17