Solve: $$ \log _{7}(2 x-1)=2 $$ A $$ 64 \frac{1}{2} $$ B $$ 63 \frac{1}{2} $$ C 25 (D) 24

Question

UpStudy AI · Accepted Answer

To solve the equation $$ \log _{7}(2x - 1) = 2 $$, follow these steps:

1. **Rewrite the logarithmic equation in its exponential form:**
   
   $$
   7^2 = 2x - 1
   $$

2. **Calculate $$ 7^2 $$:**
   
   $$
   49 = 2x - 1
   $$

3. **Solve for $$ x $$:**
   
   $$
   49 + 1 = 2x
   $$
   
   $$
   50 = 2x
   $$
   
   $$
   x = \frac{50}{2} = 25
   $$

**Answer:**  
**C) 25**
$$ x = 25 $$

Solve:
A
B
C 25
(D) 24