1 Answer

Andrea Di Giorgi · Answer 1 · 2023-05-11T03:22:58+0000

Solution

We will solve the question using the laws of logarithm

Some of the laws we will use are stated below

$\log_xa+\log_xb=\log_x(a* b)$

Also ,

$\begin{gathered} \log_xy=z \\ \\ x^z=y \end{gathered}$

Given ;

$\log_4(x-3)+\log_4(x+3)=2$

Using same logarithm base ruke , we have

$\log_4(x-3)(x+3)=2$

Removing the logarithm , we have

We can now solve the equation obtained as shown below

$\begin{gathered} 16=x^2+3x-3x-9 \\ 16=x^2-9 \\ x^2=16+9 \\ x^2=25 \\ x=\pm√(25) \\ x=\pm5 \end{gathered}$

We will ignore x is negative 5 , since we cannot have a negative logarithm

The final answer is x=5

OPTION B

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