Find the values of x so thati 27-3-27-11-275x-2

The correct option is B 165 ( 27)^ 3×( 27)^ 11 = ( 27)^5x + 2 ⇒( 27)^ 3 #160; 11 = ( 27)^5x + 2 ⇒( 27)^ 14 = ( 27)^5x + 2 ⇒ ...

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Standard XII

Mathematics

Global Maxima

Find the valu...

Question

Find the values of $x$ so that
(i) ${(\frac{2}{7})}^{- 3} \times {(\frac{2}{7})}^{- 11} = {(\frac{2}{7})}^{5 x + 2}$

\frac{13}{5}

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\frac{- 16}{5}

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\frac{12}{5}

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None of these

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Solution

The correct option is B $\frac{- 16}{5}$
${(\frac{2}{7})}^{- 3} \times {(\frac{2}{7})}^{- 11} = {(\frac{2}{7})}^{5 x + 2}$

$\Rightarrow {(\frac{2}{7})}^{- 3 - 11} = {(\frac{2}{7})}^{5 x + 2}$

$\Rightarrow {(\frac{2}{7})}^{- 14} = {(\frac{2}{7})}^{5 x + 2}$

$\Rightarrow 5 x + 2 = - 14$

$\Rightarrow 5 x = - 16$

$\Rightarrow x = \frac{- 16}{5}$

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Similar questions

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

Q. Find the value of

(1 \frac{3}{5} - \frac{2}{3} \div \frac{12}{13} + \frac{7}{5} \times \frac{1}{3})

Q. Question 11
Find the values of a and b in each of the following

(i) \frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a - 6 \sqrt{3}

(i i) \frac{3 - \sqrt{5}}{3 + 2 \sqrt{5}} = a \sqrt{5} - \frac{19}{11}

(i i i) \frac{\sqrt{2} + \sqrt{3}}{3 \sqrt{2} - 2 \sqrt{3}} = 2 - b \sqrt{6}

(i v) \frac{7 + \sqrt{5}}{7 - \sqrt{5}} - \frac{7 - \sqrt{5}}{7 + \sqrt{5}} = a + \frac{7}{11} \sqrt{5} b

Verify the following

(i) $\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}$

(ii) $\frac{- 5}{8} + \frac{- 9}{13} = \frac{- 9}{13} + \frac{- 5}{8}$

(iii) $3 + \frac{- 7}{12} = \frac{- 7}{12} + 3$

(iv) $\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}$

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Find the values of x so that(i) (27)−3×(27)−11=(27)5x+2

The correct option is B −165(27)−3×(27)−11=(27)5x+2⇒(27)−3−11=(27)5x+2⇒(27)−14=(27)5x+2⇒5x+2=−14⇒5x=−16⇒x=−165

Find the values of $x$ so that
(i) ${(\frac{2}{7})}^{- 3} \times {(\frac{2}{7})}^{- 11} = {(\frac{2}{7})}^{5 x + 2}$