Find the value of 'a' satisfying the equation ${(4^{2})}^{a} = {(7^{a})}^{2}$ [4 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Given that,

${(4^{2})}^{a} = {(7^{a})}^{2}$

$4^{2 a} = 7^{2 a}$ $[{a^{m}}^{n} = a^{m n}]$

Given, $4^{2 a} = 7^{2 a}$

Since $4 \neq 7$ the only case where the above equation is true is when both the exponents are zero.

$\Rightarrow a = 0$

$\Rightarrow 4^{2 a} = 7^{2 a} = 1$ $[∵ 4^{0} = 1, 7^{0} = 1]$

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Similar questions

Find the value of 'a' satisfying the equation.
a) ${(4^{2})}^{a} = {(7^{a})}^{2}$ .
b) $(2^{a})^{5} = 2^{4} \times 4^{3}$
[4 MARKS]

$42 A$

$+ 2 A 5 - ------ -$

$A 02$

Find the value of $A$

\frac{7 a^{2} + 2 b^{2}}{7 a^{2} - 2 b^{2}} = \frac{113}{13}

\frac{a}{b}

7 a^{2} + 7 a - 20 = 0

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