Question

2 log 3 x=4-3log3x

Answer 1

Ответ:

3

Объяснение:

В тексте задания есть число 2. Не понятно-это коэффициент, или номер?

a)  log₃x=4-3log₃x

ОДЗ: x>0

log₃x+3log₃x=4

4log₃x=4

log₃x=1

x=3^1

x=3

б) 2 log₃x=4-3log₃x

ОДЗ: x>0

2log₃x+3log₃x=4

5log₃x=4

log₃x=4/5

x=3^(4/5)

$x=\sqrt[5]{3^{4} } =\sqrt[5]{81}$

Answer 2

To solve the equation, we'll first simplify it and then find the value of 'x'.

The equation is: 2 * log3(x) = 4 - 3 * log3(x)

Step 1: Combine the logarithms on the right side of the equation. 2 * log3(x) + 3 * log3(x) = 4

Step 2: Combine the logarithms on the left side of the equation. 5 * log3(x) = 4

Step 3: Divide both sides by 5 to isolate log3(x). log3(x) = 4 / 5

Now, we need to convert the logarithmic equation to an exponential form to find the value of 'x'. Recall that in logarithmic form, log_a(b) = c is equivalent to a^c = b.

Step 4: Convert the logarithmic equation to exponential form. 3^(log3(x)) = 3^(4 / 5)

Step 5: Since 3^(log3(x)) = x, we have: x = 3^(4 / 5)

Step 6: Calculate the value of 'x': x ≈ 3^(4 / 5) ≈ 3^0.8 ≈ 2.7268

So, the approximate value of 'x' that satisfies the equation is x ≈ 2.7268.