Question

How do you solve `ln (sqrt(x+9)) = 1`?

Answer 1

`x~~-1.61`

Explanation:

`1`. Use the natural logarithmic property, `ln_color(purple)b(color(purple)b^color(darkorange)x)=color(darkorange)x`, to rewrite the right side of the equation.

`ln(sqrt(x+9))=1`

`ln(sqrt(x+9))=ln(e^1)`

`2`. Since the equation now follows a "`ln=ln`" situation, where the bases are the same on both sides, rewrite the equation without the "ln" portion.

`sqrt(x+9)=e`

`3`. Solve for `x`.

`x+9=e^2`

`x=e^2-9`

`color(green)(|bar(ul(color(white)(a/a)x~~-1.61color(white)(a/a)|)))`