Question

3log1/6x=log1/6 4+log1/6 54

Answer 1

3log1/6 x=log1/6 4+log1/6 54
Одз: x>0
3log1/6 x= log1/6 216
log1/6 x³ = log1/6 216
x³ = 216
x = 6
Ответ: 6.

Answer 2

To solve the logarithmic equation $3\log_{\frac{1}{6}}x = \log_{\frac{1}{6}}4 + \log_{\frac{1}{6}}54$, we can use the properties of logarithms to simplify and solve for $x$.

First, let's simplify the right side of the equation:

$\log_{\frac{1}{6}}4 + \log_{\frac{1}{6}}54 = \log_{\frac{1}{6}}(4 \cdot 54)$ $\log_{\frac{1}{6}}4 + \log_{\frac{1}{6}}54 = \log_{\frac{1}{6}}216$

Now we can rewrite the equation as:

$3\log_{\frac{1}{6}}x = \log_{\frac{1}{6}}216$

Using the logarithm property $\log_a(b^c) = c\log_a(b)$, we can simplify further:

$\log_{\frac{1}{6}}x^3 = \log_{\frac{1}{6}}216$

Since the bases of the logarithms are the same, we can equate the arguments:

$x^3 = 216$

Now we need to solve for $x$. Taking the cube root of both sides:

$x = \sqrt[3]{216}$

$x = 6$

So, the solution to the equation is $x = 6$.