Question

1. solve the logarithmic equation.\\(\log_{4}(3x - 2)=3\\)\

select the correct choice and, if necessary, fill in the answer box to complete your choice.\
\\(\bigcirc\\) a. the solution is \\(x = \\) \\(\square\\).\
\\(\quad\\) (type an integer or a simplified fraction.)\
\\(\bigcirc\\) b. there is no solution.

Explanation:

Step1: Convert log to exponential form

$4^3 = 3x - 2$

Step2: Calculate $4^3$

$64 = 3x - 2$

Step3: Isolate the term with x

$3x = 64 + 2$
$3x = 66$

Step4: Solve for x

$x = \frac{66}{3} = 22$

Step5: Verify the solution

Substitute $x=22$ into $3x-2$: $3(22)-2=64>0$, which is valid for logarithms.

Answer:

A. The solution is x=22.