Find the value of x for which 4-9 4 - 4-9 -7- 4-9 2x-1

( 4/9 )^4 × ( 4/9 )^ 7= ( 4/9 )^2x 1 ⇒ ( 4/9 )^4 7= ( 4/9 )^2x 1 ⇒ ( 4/9 )^ 3= ( 4/9 )^2x 1 ∴ 2x 1 = 3 ⇒ 2x= 3 +1 ⇒ 2x= 2 ⇒ x = 2/2= 1 Hence x = 1 ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with like Bases

Find the valu...

Question

Find the value of x for which ${(\frac{4}{9})}^{4} \times {(\frac{4}{9})}^{- 7} = {(\frac{4}{9})}^{2 x - 1}$

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Solution

${(\frac{4}{9})}^{4} \times {(\frac{4}{9})}^{- 7} = {(\frac{4}{9})}^{2 x - 1}$

$\Rightarrow {(\frac{4}{9})}^{4 - 7} = {(\frac{4}{9})}^{2 x - 1}$

$\Rightarrow {(\frac{4}{9})}^{- 3} = {(\frac{4}{9})}^{2 x - 1}$

$∴ 2 x - 1 = - 3 \Rightarrow 2 x = - 3 + 1$

$\Rightarrow 2 x = - 2 \Rightarrow x = \frac{- 2}{2} = - 1$

Hence x =-1

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| 7 | \times | - 4 | \times | 4 - 9 | \times | 7 | \times | - 4 | \times | 4 - 9 |

Question 94 (i)

Taking $x = \frac{- 4}{9}, y = \frac{5}{12}$ and $z = \frac{7}{18},$

Find $x + (y + z)$ .

Question 94 (k)

Taking $x = \frac{- 4}{9}, y = \frac{5}{12}$ and $z = \frac{7}{18},$ find
$x - (y + z)$

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Find the value of x for which (49)4×(49)−7=(49)2x−1

(49)4×(49)−7=(49)2x−1 ⇒(49)4−7=(49)2x−1 ⇒(49)−3=(49)2x−1 ∴2x−1=−3⇒2x=−3+1 ⇒2x=−2⇒x=−22=−1 Hence x =-1

Find the value of x for which ${(\frac{4}{9})}^{4} \times {(\frac{4}{9})}^{- 7} = {(\frac{4}{9})}^{2 x - 1}$