Question

6. If (9/7)^3 (49/81)^2x-6 =(7/9)^9 the value of x is:
(a) 12
(6) 9
(c) 8
(d) 6​

Answer 1

Answer:

(d) 6

Step-by-step explanation:

Taking (9/7)³ to R.H.S. will change it to (7/9)³ and rearranging (49/81) as (7/9)² we will have :

${( { \frac{7}{9} }^{2} } )^{2x - 6 } = ( { \frac{7}{9} }^{9} )( \frac{7}{9}^{3} ) \\ = { \frac{7}{9}}^{4x - 12 } = { \frac{7}{9} }^{9 + 3}$

now, equating the powers we have,

4x - 12 = 12

or, 4x = 12+12 = 24

or, X = 24/4 = 6

Answer 2

Option D) 6

Step-by-step explanation:

We are given the following in the question:

$\bigg(\displaystyle\frac{9}{7}\bigg)^3\bigg(\frac{49}{81}\bigg)^{2x-6} = \bigg(\frac{7}{9}\bigg)^9$

Exponential properties:

$a^m a^n = a^{m+n}\\\\\dfrac{a^m}{a^n}= a^{m-n}\\\\(a^m)^n = a^{mn}$

Using properties, we can write:

$\bigg(\displaystyle\frac{9}{7}\bigg)^3\bigg(\frac{49}{81}\bigg)^{2x-6} = \bigg(\frac{7}{9}\bigg)^9\\\\\bigg(\displaystyle\frac{7}{9}\bigg)^{-3}\bigg(\frac{7^2}{9^2}\bigg)^{2x-6} = \bigg(\frac{7}{9}\bigg)^9\\\\\bigg(\displaystyle\frac{7}{9}\bigg)^{-3}\bigg(\frac{7}{9}\bigg)^{4x-12} = \bigg(\frac{7}{9}\bigg)^9\\\\\bigg(\displaystyle\frac{7}{9}\bigg)^{4x-12-3} = \bigg(\frac{7}{9}\bigg)^9\\\\4x-15 = 9\\4x = 24\\x = 6$

Thus, the correct answer is

Option D) 6

#LearnMore

Simplify the following and write the answer in the exponential form: 3 to the power 2 × 1/3 to the power 5 × ( 3 to the power 3 ) to the power 4

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