Question

if (5/2)² × (5/2)a+5 = (5/2)⁸, then find 'a'​

Answer 1

Given -

$( { \frac{5}{2} })^{2} \times ({ \frac{5}{2} })^{a + 5} = ({ \frac{5}{2} })^{8}$

To find -

• The value of a

Solution -

$\implies( {\frac{5}{2} })^{2} \times ({ \frac{5}{2} })^{a + 5} = ({ \frac{5}{2} })^{8}$

$\implies ({ \frac{5}{2} })^{2 + a + 5} = ({ \frac{5}{2} })^{8}$

$\implies({ \frac{5}{2} })^{7 + a} = ({ \frac{5}{2} })^{8}$

$\implies7 + a = 8$

$\implies \: a = 8 - 7$

$\implies \: a = 1$

Therefore the value of a is 1

Verification

$\implies ({ \frac{5}{2} })^{2} \times ({ \frac{5}{2} })^{a + 5} = ({ \frac{5}{2} })^{8}$

Putting the value of a =1 we will get -

$\implies ({ \frac{5}{2} })^{2} \times ({ \frac{5}{2} })^{1 + 5} = ({ \frac{5}{2} })^{8}$

$\implies ({ \frac{5}{2} })^{2} \times ({ \frac{5}{2} })^{6} =( { \frac{5}{2} })^{8}$

$\implies( { \frac{5}{2} })^{2 + 6} =( { \frac{5}{2} })^{8}$

$\implies ({ \frac{5}{2} })^{8} = ({ \frac{5}{2} })^{8}$

L. H. S = R. H. S

Hence, verified

Answer 2

Question:

if (5/2)² × (5/2)a+5 = (5/2)⁸, then find 'a'

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Solution:

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$\tt { \dfrac {5}{2}^{2} \times \dfrac{5}{2} ^{a+5} = \dfrac {5}{2}^{8} }$

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$\boxed {\bf Using \: identity : a^m \times a^n = a^{m+n} }$

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$: \implies \tt { \dfrac{5}{2}^{2 + a + 5} = \dfrac {5}{2}^{8} }$

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$: \implies \tt {\dfrac {5}{2} ^{7+a} = \dfrac {5}{2}^{8}}$

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$: \implies \tt { 7 + a = 8}$

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$: \implies \tt {a = 1}$

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