Question

I need help ASAP, thanks

Answer 1

x = 4 or x = -9

Explanation:

As you can see from the question provided, you were given the following logarithms equation

`\log _6x+log_6(x\text{ + 5) = 2}`

Recall that,

`\text{Log}_xA+log_xB=Log_x(A\text{ x B)}`
`\begin{gathered} \text{Let} \\ \log _xA=log_6x \\ \log _xB=log_6(x\text{ + 5)} \end{gathered}`

The next thing is to replace the values and simplify

As you can see from the last process, the logarithms function resulted in a quadratic equation.

The next thing is to solve the equation using the factorization method.

Note that, the general quadratic function is given below as

`ax^2\text{ + bx + c = 0}`

Relating the two equations, you will have the following data

• a = 1

,

• b = 5

,

• c = -36

The next thing is to find the value of ac

`\begin{gathered} ac\text{ = 1 }\cdot\text{(-36)} \\ ac\text{ = -36} \end{gathered}`
`\begin{gathered} x^2\text{ -4x + 9x - 36 = 0} \\ x(x\text{ - 4) + 9(x - 4) = 0} \\ (x\text{ - 4) (x + 9) = 0} \\ (x\text{ - 4) = 0 or (x + 9) = 0} \\ x\text{ - 4 = 0 or x + 9 = 0} \\ x\text{ = 0 + 4 or x - 9 = 0} \\ x\text{ = 4 or x =-9} \end{gathered}`

Hence, the values of x are 4 and -9