Question

Find x such that 3 power x + 2 = 3 power x +216

Answer 1

Answer:

The value of x is 3

Step-by-step explanation:

Given phrase,

3 power x + 2 = 3 power x +216

$\implies 3^{x+2}=3^{x}+216$

$3^{x}.3^2 = 3^x+216$     (using $a^{m+n}=a^m.a^n$)

$3^x.3^2 - 3^x = 216$

$3^x(9-1) = 216$

$3^x(8) = 216$

$3^x = 27$

$3^x = 3^3$

Comparing the powers,

x = 3

Hence, the value of x would be 3.

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Answer 2

The value of x is 3.

Step-by-step explanation:

The given equation is

$3^{x+2}=3^x+216$

Using the product property of exponents the given equation can be rewritten as

$3^{x}\cdot 3^{2}=3^x+216$          $[\because a^{m+n}=a^ma^n]$

Subtract $3^x$ on both sides.

$3^{x}\cdot 9-3^x=216$

Taking out common factors.

$3^{x}(9-1)=216$

$3^{x}(8)=216$

Divide both sides by 8.

$3^{x}=27$

$3^{x}=3^3$

On comparing both sides we get

$x=3$

Therefore, the value of x is 3.

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