Question

Iog 3 x =  Iog 3 6 + Iog 3  2​

Answer 1

Ответ:

384

Объяснение:

1) Логарифм произведения равен сумме логарифмов.

Следовательно, правая часть уравнения первоначально имела вид:

Iog (36 * 32).

2) Iog 3 x =  Iog (36 * 32)

Iog 3 x =  Iog 1152,

откуда

3 x  = 1152,

х = 384.

Ответ: х = 384

Answer 2

To solve the equation, let's simplify the expressions using the properties of logarithms. The logarithm base 3 of a number x can be written as log₃(x).

Using the logarithmic property logₐ(m) + logₐ(n) = logₐ(m * n), we can rewrite the equation as:

log₃(x) = log₃(6) + log₃(2)

Next, we can simplify the right side using the property logₐ(m) + logₐ(n) = logₐ(m * n):

log₃(x) = log₃(6 * 2)

Simplifying further:

log₃(x) = log₃(12)

Since the logarithm base 3 of both sides are equal, the argument inside the logarithm must be equal as well:

x = 12

Therefore, the solution to the equation is x = 12.