Question

Log3 X= log3 2-4 log9 5

Answer 1

ОДЗ: x>0
Log3 X= log3 2-(4*1/2)* log3 5
Log3 X= log3 2-log3 25
Log3 X= log3 2/25
X=2/25 - подходит по ОДЗ Ответ: 2/25.

Answer 2

To solve the equation log₃(x) = log₃(2) - 4 * log₉(5), we can use logarithmic properties and change the base of the second logarithm to match the base of the first logarithm.

First, recall the change of base formula for logarithms:

logₐ(b) = logₓ(b) / logₓ(a)

We'll change the base of the second logarithm from 9 to 3:

log₉(5) = log₃(5) / log₃(9)

Now, we know that log₃(9) = 2 because 3² = 9. So, we can simplify:

log₉(5) = log₃(5) / 2

Now, we can rewrite the equation with a common base:

log₃(x) = log₃(2) - 4 * (log₃(5) / 2)

Next, apply the properties of logarithms:

log₃(x) = log₃(2) - 2 * log₃(5)

Now, we can use the property that states that if logₐ(b) = logₐ(c), then b = c:

x = 2 - 2 * 5

x = 2 - 10

x = -8

So, the solution to the equation log₃(x) = log₃(2) - 4 * log₉(5) is x = -8.