Q 98.

Solve the equation.

$\log_{6} 36 = 5 x + 3$

Verified

Answer

The solution to the equation, $\log_{6} 36 = 5 x + 3$ is, $x = - \frac{1}{5}$ .

1Step 1. Given Information

The given equation to be solved is $\log_{6} 36 = 5 x + 3$ .

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 $\log_{6} 36 = 5 x + 3$ .

Use rule of change from logarithm to exponents:

$\log_{6} 36 = 5 x + 3 6^{5 x + 3} = 36 (6)^{5 x + 3} = (6)^{2} 5 x = - 1 x = - \frac{1}{5}$

The solution to the given equation is, $x = - \frac{1}{5}$ .