Question

c. $2 - 2log_{11} (10 - 6x) = 6$

Explanation:

Step1: Isolate the logarithmic term

Subtract 2 from both sides.
$2 - 2\log_{11}(10-6x) - 2 = 6 - 2$
$-2\log_{11}(10-6x) = 4$

Step2: Solve for the logarithm

Divide both sides by -2.
$\frac{-2\log_{11}(10-6x)}{-2} = \frac{4}{-2}$
$\log_{11}(10-6x) = -2$

Step3: Convert to exponential form

Use $\log_b(a)=c \implies b^c=a$.
$11^{-2} = 10 - 6x$

Step4: Calculate $11^{-2}$

Simplify the exponential expression.
$\frac{1}{11^2} = 10 - 6x$
$\frac{1}{121} = 10 - 6x$

Step5: Isolate the x term

Subtract 10 from both sides.
$\frac{1}{121} - 10 = -6x$
$\frac{1 - 1210}{121} = -6x$
$-\frac{1209}{121} = -6x$

Step6: Solve for x

Divide both sides by -6.
$x = \frac{-\frac{1209}{121}}{-6}$
$x = \frac{1209}{121 \times 6}$
$x = \frac{403}{242}$

Answer:

$x = \frac{403}{242}$