Question

solve for x. \\(\log_3 (4x - 19) = 4\\) \\(x = \square\\)

Explanation:

Step1: Convert log to exponential form

$\log_b(a)=c \implies b^c=a$, so $3^4 = 4x - 19$

Step2: Calculate $3^4$

$3^4 = 81$, so $81 = 4x - 19$

Step3: Isolate the term with $x$

Add 19 to both sides: $81 + 19 = 4x$
$100 = 4x$

Step4: Solve for $x$

Divide by 4: $x = \frac{100}{4}$

Answer:

$x = 25$