Question

log(10 - 6x) = 2

Explanation:

Step1: Convert logarithmic to exponential form

Assuming the logarithm is base 10 (common logarithm), if $\log_{10}(a)=b$, then $a = 10^b$. Here, $\log(10 - 6x)=2$, so we can rewrite it as $10 - 6x=10^2$.
$$10 - 6x = 100$$

Step2: Solve for x

Subtract 10 from both sides:
$$-6x=100 - 10$$
$$-6x = 90$$
Divide both sides by - 6:
$$x=\frac{90}{-6}$$
$$x=- 15$$

Step3: Check the domain

The argument of the logarithm must be positive. For $\log(10 - 6x)$, we need $10-6x>0$. Substitute $x = - 15$: $10-6\times(-15)=10 + 90=100>0$, which is valid.

Answer:

$x=-15$