Solve for x in the equation 3-2-x- - 3-1-x- - 2916- nbsp-4567

The correct option is B 5We have 3^(2+x) + 3^(1+x) = 2916. ⇒ 3^2 × 3^x+3^1 × 3^x = 2916 (∵ a^m+n = a^m × a^n) i.e., 9 nbsp;× 3^x+3 × 3^x = 2916 ⇒ 3^x(9 ...

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Standard VII

Mathematics

Product Rule of Exponents

Solve for x i...

Question

Solve for $x$ in the equation $3^{(2 + x)} + 3^{(1 + x)} = 2916.$

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Solution

The correct option is B 5
We have $3^{(2 + x)} + 3^{(1 + x)} = 2916.$
$\Rightarrow 3^{2} \times 3^{x} + 3^{1} \times 3^{x} = 2916 (∵ a^{m + n} = a^{m} \times a^{n})$
i.e., $9 \times 3^{x} + 3 \times 3^{x} = 2916$
$\Rightarrow 3^{x} (9 + 3) = 2916$
$\Rightarrow 3^{x} = \frac{2916}{12} = 243$
$\Rightarrow 3^{x} = 3^{5}$
Since the powers on both sides have equal bases, they must have equal exponents as well.
$∴ x = 5$

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Solve for x in the equation 3(2+x)+3(1+x)=2916.

The correct option is B 5We have 3(2+x)+3(1+x)=2916. ⇒32×3x+31×3x=2916 (∵am+n=am×an) i.e., 9×3x+3×3x=2916 ⇒3x(9+3)=2916 ⇒3x=291612=243 ⇒3x=35 Since the powers on both sides have equal bases, they must have equal exponents as well. ∴x=5

Solve for $x$ in the equation $3^{(2 + x)} + 3^{(1 + x)} = 2916.$