Question

1. solve the equation for x. \\(\log_{6}(6x - 1) = 1\\) select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\(\bigcirc\\) a. \\(x = \square\\) (simplify your answer.) \\(\bigcirc\\) b. there is no solution.

Explanation:

Step1: Convert log to exponential form

Recall $\log_b(a)=c$ means $b^c=a$. So:
$$6^1 = 6x - 1$$

Step2: Simplify and solve for x

Calculate $6^1=6$, then isolate $x$:
$$6 = 6x - 1$$
$$6 + 1 = 6x$$
$$7 = 6x$$
$$x = \frac{7}{6}$$

Step3: Verify domain

Check $6x-1>0$: $6(\frac{7}{6})-1=7-1=6>0$, which is valid.

Answer:

A. $x=\frac{7}{6}$ (Simplify your answer.)