Question

what will be x' s value...?​

Answer 1

Question:

Find the value of x.

$\displaystyle{\sf\:3\:\times\:27^x\:=\:9^{x\:+\:4}}$

Answer:

The value of x is 7.

Step-by-step-explanation:

The given equation is

$\displaystyle{\sf\:3\:\times\:27^x\:=\:9^{x\:+\:4}}$

We have to find the value of x.

Now,

$\displaystyle{\sf\:3\:\times\:27^x\:=\:9^{x\:+\:4}}$

$\displaystyle{\implies\sf\:3\:\times\:(\:3^3\:)^x\:=\:(\:3^2\:)^{x\:+\:4}}$

We know that,

$\displaystyle{\boxed{\pink{\sf\:(\:a^m\:)^n\:=\:a^{m\:\times\:n}\:}}}$

$\displaystyle{\implies\sf\:3\:\times\:3^{3x}\:=\:3^{2\:(\:x\:+\:4\:)}}$

$\displaystyle{\implies\sf\:3\:\times\:3^{3x}\:=\:3^{2x\:+\:8}}$

We know that,

$\displaystyle{\boxed{\blue{\sf\:a^m\:\times\:a^n\:=\:a^{m\:+\:n}}}}$

$\displaystyle{\implies\sf\:3^{1\:+\:3x}\:=\:3^{2x\:+\:8}}$

Bases are equal, so powers should be also equal.

$\displaystyle{\therefore\:\sf\:1\:+\:3x\:=\:2x\:+\:8}$

$\displaystyle{\implies\sf\:3x\:-\:2x\:=\:8\:-\:1}$

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:x\:=\:7\:}}}}$

∴ The value of x is 7.

Answer 2

7

$\huge\green{Given:-}$

$3 \times {27}^{x} = {9}^{x + 4}$

$\huge\red{To \: Find:-}$

$value \: of \: x$

$\huge\blue{Solution : }$

$3 \times {27}^{x} = {9}^{x + 4}$

$3 \times( {3}^{3} ) {}^{x} = ( {3}^{2} ) {}^{x + 4}$

• We know:-

$\huge\green{( {a}^{m} ) {}^{n} = {a}^{mn} }$

$3 \times {3}^{3x} = {3}^{2(x + 4)}$

$3 \times {3}^{3x} = {3}^{2x + 8}$

• We know:-

$\huge\pink{ {a}^{m} \times {a}^{n} = {a}^{m + n} }$

${3}^{1 + 3x \: \: = \: \: \: {3}^{2x + 8} }$

$1 + 3x = 2x + 8$

$3x - 2x = 8 - 1$

$x = 7$

Hence, the value of x is 7.

$\huge\red{Thank \: You}$