Question

What is x if `lnx + ln5x^2 = 10`?

Answer 1

First, you should use the logarithm rule
`log_a (x) + log_a (y) = log_a ( x * y)`

Here, it gives you:
`" ln x + ln 5 x^2 = 10`
`<=> " ln( x * 5 x^2) = 10`
`<=> " ln(5 x^3) = 10`

Now, you can exponentiate both sides to get rid of the `ln`:

`<=> " e^(ln(5x^3)) = e^10`

... remember that `e` and `ln` are inverse functions...

`<=> " 5x^3 = e^10`
`<=> " x^3 = (e^10) / 5`
`<=> " x = root(3)((e^10) / 5)`