If $$ \log _{3}(7 x-2)=5 $$, then what is the value of $$ x ? $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ \log_{3}(7x - 2) = 5 $$, we'll use the definition of logarithms:

$$
\log_{b}(A) = C \quad \text{means} \quad b^C = A
$$

Applying this to the given equation:

$$
\log_{3}(7x - 2) = 5 \quad \Rightarrow \quad 3^5 = 7x - 2
$$

Calculate $$ 3^5 $$:

$$
3^5 = 243
$$

So,

$$
243 = 7x - 2
$$

Add 2 to both sides:

$$
245 = 7x
$$

Finally, divide both sides by 7 to solve for $$ x $$:

$$
x = \frac{245}{7} = 35
$$

**Answer:** 35
$$ x = 35 $$

If , then what is the value of