Question

Log49 (100-99x) = log49 (101-x) +1 49 - основание логарифма. Ответ: -96,98

Answer 1

Надеюсь все понятно)

Answer 2

To solve the logarithmic equation, we'll first apply the basic properties of logarithms to simplify the equation and then find the value of x.

The basic property of logarithms states that log_b(m) - log_b(n) = log_b(m/n).

Given equation: log49(100 - 99x) = log49(101 - x) + 1

Now, using the property, we can rewrite the equation as follows:

log49(100 - 99x) - log49(101 - x) = 1

Next, we'll use another property of logarithms: If log_b(a) = c, then b^c = a.

Applying this property, we get:

49^(log49(100 - 99x) - log49(101 - x)) = 49^1

Now, we can simplify the equation further:

(100 - 99x) / (101 - x) = 49

Now, we'll solve for x:

100 - 99x = 49(101 - x)

100 - 99x = 4949 - 49x

-99x + 49x = 4949 - 100

-50x = 4849

x = 4849 / -50

x ≈ -96.98

So, the value of x is approximately -96.98.