Question

if 3^ x × 9 = 3⁴ find the value of x​

Answer 1

Answer:

x=2

Step-by-step explanation:

Question:

$\sf{If\:3^x × 9 = 3⁴, \:find \:the\: value \:of\: x}$

Given:

$3^x × 9 = 3⁴$

To find:

The value of x.

Solution:

$\mathtt{3^x × 9 = 3⁴}$

Here, 9 can be written as $3^2$

So, $\mathtt{3^x × 3^2 = 3⁴}$

Remember:

Law of exponents: $a^m × a^n=\:a^{(m+n)}$

Now, let's continue.......

$\mathtt{3^{(x+2)}= 3⁴}$

3 gets cancelled,

$\mathtt{ \cancel3^{(x+2)}= \cancel3⁴}$

Now, the equation would be:-

• x+2=4
• x=4-2
• $\implies\boxed{\frak{\purple{x=2}}}$

Therefore, the value of x is 2.

Now let's verify:

Verification:

$\mathtt{3^x × 9 = 3⁴}$

Substitute the value of x=2.....

$\mathtt{3^2 × 9 = 3⁴}$

$\mathtt{9 × 9 = 3⁴}$

$\mathtt{81 = 3⁴}$

$\mathtt{ 3⁴= 3⁴}$

Hence, verified.

Answer 2

$\sf\Large{\underline{\underline{Question}}}:-$

$\sf\large\: If \: 3{}^{x} × 9 = 3{}^{4}$

Find the value of x.

$\sf\Large{\underline{\underline{Answer}}}:-$

Given:-

$\sf\large\: 3{}^{x} × 9 = 3{}^{4}$

To find:-

The value of x

Solution:-

$\sf\large\implies \: 3{}^{x} × 9 = 3{}^{4}$

$\sf\large\implies \: 3{}^{x} × 3{}^{2} = 3{}^{4}$

Since, 3² = 9

$\sf\large\implies \: 3{}^{x + 2} = 3{}^{4}$

$\sf\large\implies \: x + 2 = 4$

$\sf\large\implies \: x = 4 - 2$

$\sf\large{\boxed{ x = 2 }}$

$\sf{\red{\therefore{\boxed{Hence, \: the \: of \: x = 2}}}}$

$\pink{Hope \: it \: helps}$