Question

Log 16 X+log 8 X+log 2 X=19\ 36

Answer 1

ОДЗ  х>0.   ∛2>0

Log 16 X+log 8 X+log 2 X=19\ 36

Answer 2

It looks like you have an equation involving logarithms that you'd like to solve for the variable "X". The equation you provided is:

log₁₆(X) + log₈(X) + log₂(X) = 19/36

To solve this equation, we can use logarithmic properties to simplify and combine the logarithmic terms. One important property is the logarithm change of base formula:

logₐ(b) = logₓ(b) / logₓ(a)

Applying this property to the given equation:

log₁₆(X) + log₈(X) + log₂(X) = 19/36

We can change the bases of the logarithms to a common base, such as 2:

(log₂(X) / log₂(16)) + (log₂(X) / log₂(8)) + log₂(X) = 19/36

Now, simplify the fractions by expressing 16 and 8 as powers of 2:

(log₂(X) / 4) + (log₂(X) / 3) + log₂(X) = 19/36

To combine the fractions, find a common denominator, which is 12:

(3 * log₂(X) + 4 * log₂(X) + 12 * log₂(X)) / 12 = 19/36

(19 * log₂(X)) / 12 = 19/36

Now, solve for log₂(X):

log₂(X) = (19/36) * (12/19)

log₂(X) = 0.5

Now, we need to solve for X. Recall that log₂(X) = 0.5 can be rewritten as an exponential equation:

X = 2^(0.5)

X = √2

So, the solution for the equation log₁₆(X) + log₈(X) + log₂(X) = 19/36 is X = √2.