You need to rewrite the term `lg(x^5)` using the power property of logarithms, such that:

`lg^2 x + 5lg x - 6 = 0`

You should come up with the notation ` lg x = y` , such that:

`y^2 + 5y - 6 = 0`

You need to use quadratic formula, such that:

`y_(1,2) = (-5+-sqrt(25 + 24))/2 => y_(1,2) = (-5+-sqrt49)/2`

`y_1 = 1; y_2 = -6`

You need to solve for `x` the following equations, such that:

`lg x = 1 => x = 10^1 => x = 10`

`lg x = -6 => x = 10^(-6) => x = 1/10^6 `

**Hence, evaluating the solutions to the given equation, yields **`x = 1/10^6 , x = 10.`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now