# Help me tO solve this algebra..please

• Dec 9th 2012, 12:27 AM
sharmala
Help me tO solve this algebra..please
Solve 3 In 2x =3 + In 27
• Dec 9th 2012, 12:39 AM
MarkFL
Re: Help me tO solve this algebra..please
I am assuming you mean $\displaystyle \ln$ and not $\displaystyle \text{In}$. We are given:

$\displaystyle 3\ln(2x)=3+\ln(27)$

I would rewrite this as:

$\displaystyle 3\ln(2x)=3+\ln(3^3)$

so that we may use the property $\displaystyle \log_a(b^c)=c\cdot\log_a(b)$ to then rewrite the equation as:

$\displaystyle 3\ln(2x)=3+3\ln(3)$

Next, divide through by 3:

$\displaystyle \ln(2x)=1+\ln(3)$

Next, use the fact that $\displaystyle \ln(e)=1$ to write:

$\displaystyle \ln(2x)=\ln(e)+\ln(3)$

To finish now, on the right use the property $\displaystyle \log_a(b)+\log_a(c)=\log_a(bc)$, then equate the resulting arguments, then solve for $\displaystyle x$.
• Dec 9th 2012, 01:02 PM
bjhopper
Re: Help me tO solve this algebra..please
another method
3ln(2x) =3 +ln(27)
ln (2x/3)^3 =3
e^3 =(2x/3)^3
e = 2x/3
e = 2.303