Find value of n

**Mukilab** · January 7th 2010, 09:30 AM

No calculator, method not answer please

$3\cdot \sqrt{27}=3^{n}$

**Dinkydoe** · January 7th 2010, 10:03 AM

Divide both sides by 3 to obtain: $\sqrt{27} = 3^{n-1}$

Now take the square of both sides to get: $27 = 3^{2(n-1)}$

We know that $27 = 3^3 = 3^{2(n-1)}$ so $3 = 2(n-1)$ .

This gives: $5 = 2n$ so $\frac{5}{2} = n$
(you can ofcourse save some steps: $3\cdot \sqrt{27} = 3\cdot \sqrt{3^3} = 3^{\frac{3}{2}+1} = 3^{\frac{5}{2}} \rightarrow n = \frac{5}{2}$ )

**Mukilab** · January 7th 2010, 10:37 AM

Originally Posted by Dinkydoe

Divide both sides by 3 to obtain: $\sqrt{27} = 3^{n-1}$

Now take the square of both sides to get: $27 = 3^{2(n-1)}$

We know that $27 = 3^3 = 3^{2(n-1)}$ so $3 = 2(n-1)$ .

This gives: $5 = 2n$ so $\frac{5}{2} = n$
(you can ofcourse save some steps: $3\cdot \sqrt{27} = 3\cdot \sqrt{3^3} = 3^{\frac{3}{2}+1} = 3^{\frac{5}{2}} \rightarrow n = \frac{5}{2}$ )

How did you get 3=2(n-1) from $3^{2(n-1)}??/$

**Dinkydoe** · January 7th 2010, 10:43 AM

if $3^3 = 3^{2(n+1)}$ this means that $3 = 2(n+1)$

Since $a^b = a^c \rightarrow b = c$

**Mukilab** · January 7th 2010, 12:15 PM

Thanks for the formula I can add to my list!

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