Question

date:
course: math 120 spring 2006 section 8011
assignment:

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=)
(type an integer or a simplified fraction.)
(\bigcirc) b. there is no solution.

1. solve the equation for (x).

Explanation:

Step1: Rewrite 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 original equation: $\log_4(3*22 - 2) = \log_4(64) = 3$, which is valid.

Answer:

A. The solution is $x=22$