natural log

[alyren]

solve equation.

2ln2x = 18

is this right?

1).divided 2 both side

2).LNx=9

3).e^9=x

also need help on how to solve this equation

find k such that f(x)=x^3-kx^2+kx+2 has the factor x-2

 

[galactus]

solve equation.

2ln2x = 18

is this right?

1).divided 2 both side

2).LNx=9

3).e^9=x

You forgot to divide by 2. Other than that, it's good.

find k such that f(x)=x^3-kx^2+kx+2 has the factor x-2

Since k-2 is a factor, then x=2 must make f(x)=0

Sub x=2 into the expression and set equal to 0. It is now an equation. Solve for k.

 

[lookagain]

solve equation.

2ln2x = 18

is this right?

1).divided 2 both side

2).LNx=9

3).e^9=x

alyren, when you divide both sides by 2, you don't divide the "2x" (that you are taking the log of) by 2.

\(\displaystyle 2ln(2x) = 18\)

\(\displaystyle 2\log_e(2x) = 18\) . . . . (optional equivalent equation)

Divide by 2 on each side:

\(\displaystyle \log_e(2x) = 9\)

Rewrite as an equivalent exponential equation:

\(\displaystyle 2x = e^9\)

Divide each side by 2:

\(\displaystyle x = \frac{e^9}{2}\)