In the given equation the value of x is 17-5 9 - 3x-272 x-5A- i- 1-54 - 109- ii- 1-6 - 10-7B- i- 1-54 - 103- ii- 1-6 - 107

The correct option is B i. 1.54 x 103, ii. 1.6x107 Given 9 × 3^x = (27)^2x 5 ⇒ 3^2 × 3^x = (3^3)^2x 5 ⇒ 3^x + 2 = 3^3(2x 5) Since bases are equal, powe ...

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Standard VIII

Mathematics

Power of a Power

In the given ...

Question

In the given equation the value of $x$ is $\frac{17}{5}$

$9 \times 3^{x} = (27)^{2 x - 5}$

i. 1.54 x 10³, ii. 1.6x10⁷

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i. 1.54x10⁹, ii. 1.6x10^-7

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Solution

The correct option is A
i. 1.54 x 10³, ii. 1.6x10⁷

Given

$9 \times 3^{x} = (27)^{2 x - 5}$

$\Rightarrow$ $3^{2} \times 3^{x} = (3^{3})^{2 x - 5}$

$\Rightarrow$ $3^{x + 2} = 3^{3 (2 x - 5)}$

Since bases are equal, powers may also be equal.

$x + 2 = 6 x - 15$

$\Rightarrow x = \frac{17}{5}$

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9 \times 10^{9} \times \frac{1.6 \times 10^{- 19} \times 1.6 \times 10^{- 19}}{(5.3 \times 10^{- 11})^{2}} .

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Question 109

In the given figures (i) and (ii), find the values of a, b and c.

The standard exponential form of 1,540,000,000 is 1.54 x 10 $^{9}$ .

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In the given equation the value of x is 175 9×3x = (27)2x−5

The correct option is A i. 1.54 x 103, ii. 1.6x107 Given 9×3x = (27)2x−5 ⇒ 32×3x=(33)2x−5 ⇒ 3x+2=33(2x−5) Since bases are equal, powers may also be equal. x+2=6x−15 ⇒ x=175

In the given equation the value of $x$ is $\frac{17}{5}$

$9 \times 3^{x} = (27)^{2 x - 5}$

The correct option is A
i. 1.54 x 10³, ii. 1.6x10⁷

Given

$9 \times 3^{x} = (27)^{2 x - 5}$

$\Rightarrow$ $3^{2} \times 3^{x} = (3^{3})^{2 x - 5}$

$\Rightarrow$ $3^{x + 2} = 3^{3 (2 x - 5)}$

Since bases are equal, powers may also be equal.

$x + 2 = 6 x - 15$

$\Rightarrow x = \frac{17}{5}$