Question 177iiFind x- 2-52x - 6- 2-53 - 2-5x - 2

We have, ( 2/5)^2x + 6×( 2/5)^3 = ( 2/5)^x + 2 Using law of exponents, a^m + a^n = (a)^m + n Then, ( 2/5)^(2x + nbsp;6) + 3 = ( 2/5)^x + 2 Then, ( 2/5)^2x ...

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Standard VIII

Mathematics

Power of a Power

Question 177i...

Question

Question 177(ii)

Find x.
${(\frac{2}{5})}^{2 x + 6} \times {(\frac{2}{5})}^{3} = {(\frac{2}{5})}^{x + 2}$

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Solution

We have, ${(\frac{2}{5})}^{2 x + 6} \times {(\frac{2}{5})}^{3} = {(\frac{2}{5})}^{x + 2}$
Using law of exponents, $a^{m} + a^{n} = (a)^{m + n}$

$T h e n, {(\frac{2}{5})}^{(2 x + 6) + 3} = {(\frac{2}{5})}^{x + 2}$

$T h e n, {(\frac{2}{5})}^{2 x + 9} = {(\frac{2}{5})}^{x + 2}$

Since the base are same on both sides, we can equate the powers.
On equating the powers of $(\frac{2}{5})$ , we get

2x + 9 = x + 2
$\Rightarrow$ 2x -x = 2 - 9
$\Rightarrow$ x = -7

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Similar questions

Question 177(ii)

Find x.
${(\frac{2}{5})}^{2 x + 6} \times {(\frac{2}{5})}^{3} = {(\frac{2}{5})}^{x + 2}$

Q. Solve:

5^{2 x} = 3^{2 x} + 2 \cdot 5^{x} + 2 \cdot 3^{x}

Q. Solve

6 (1 - 4 x) + 7 (2 + 5 x) = 53

for the value of

x

Q. Factorize

:

(i)

x^{2} + 5 x + 6 = 0

(ii)

x^{2} - 5 x + 6 = 0

(iii)

x^{2} + 5 x - 6 = 0

(iv)

x^{2} - 5 x - 6 = 0

Q. If

| x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}

, then

x \in

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Question 177(ii) Find x. (25)2x+6×(25)3=(25)x+2

We have, (25)2x+6×(25)3=(25)x+2 Using law of exponents, am+an=(a)m+n Then, (25)(2x+6)+3=(25)x+2 Then, (25)2x+9=(25)x+2 Since the base are same on both sides, we can equate the powers. On equating the powers of (25), we get 2x + 9 = x + 2 ⇒ 2x -x = 2 - 9 ⇒ x = -7

Question 177(ii)

Find x.
${(\frac{2}{5})}^{2 x + 6} \times {(\frac{2}{5})}^{3} = {(\frac{2}{5})}^{x + 2}$