Q 89.

Solve the equation.

$\log_{2} (2 x + 1) = 3$

Verified

Answer

The solution to the equation, $\log_{2} (2 x + 1) = 3$ is, $x = 3.5$ .

1Step 1. Given Information

The given equation to be solved is $\log_{2} (2 x + 1) = 3$ .

2Step 2. Formula used

Rule of change from logarithm to exponents:

$\log_{a} b = y \Rightarrow a^{y} = b$

3Step 3. Finding Solution

The given equation is $\log_{2} (2 x + 1) = 3$ .

Use rule of change from logarithm to exponents:

$\log_{2} (2 x + 1) = 3 2 x + 1 = 2^{3} 2 x = 8 - 1 x = \frac{7}{2} x = 3.5$

The solution to the given equation is, $x = 3.5$ .