Question

√3^n =729 what is the value of
n

Answer 1

Answer:

12

Step-by-step explanation:

Given that $\sqrt{3^{n} }= 729$

$\sqrt{3^{n} } \: can \: be \: written \:as \: 3^{\frac{n}{2} }$

as, $\sqrt{x} = x^{\frac{1}{2} }$

So, we get that

$3^{\frac{n}{2} }= 729$

Again, 729 can be written as 3⁶

So, $3^{\frac{n}{2} } = 3^{6}$

Now since bases are same, we can directly compare the exponents

We get, n/2 = 6

Cross multiplying, we get

n = 6 × 2

n = 12

Answer 2

Answer:

12

Step-by-step explanation:

Given that \begin{gathered}\sqrt{3^{n} }= 729 \\\end{gathered}

3

n

=729

\begin{gathered}\sqrt{3^{n} } \: can \: be \: written \:as \: 3^{\frac{n}{2} } \\\end{gathered}

3

n

canbewrittenas3

2

n

as, \begin{gathered}\sqrt{x} = x^{\frac{1}{2} } \\\end{gathered}

x

=x

2

1

So, we get that

\begin{gathered}3^{\frac{n}{2} }= 729\\ \\\end{gathered}

3

2

n

=729

Again, 729 can be written as 3⁶

So, \begin{gathered}3^{\frac{n}{2} } = 3^{6}\\ \\\end{gathered}

3

2

n

=3

6

Now since bases are same, we can directly compare the exponents

We get, n/2 = 6

Cross multiplying, we get

n = 6 × 2

n = 12