Find the value of n when- 52n- 53-59

5^2n×5^3 = 5^9 ⇒5^2n + 3 = 5^9 By equating powers ⇒ 2n + 3 = 9 ⇒ 2n = 9 3 ⇒ n = 62 = 3 ...

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Find the valu...

Question

Find the value of $n$ when:
$5^{2 n} \times 5^{3} = 5^{9}$

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Solution

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5^{2 n} \times 5^{3} = 5^{9}

8 \times 2^{n + 2} = 32

n

{(\frac{4}{5})}^{3} \times {(\frac{4}{5})}^{- 6} = {(\frac{4}{5})}^{2 n - 1}

$b)$

n (3^{- 5}) = 3

$c)$

n {(- 5)}^{4} \div n^{2} = 5

5^{n} \div 5^{3} = 5^{7}

n

5^{2 n} \times 5^{3} = 5^{11}

9 \times 3^{n} = 3^{7}

8 \times 2^{n + 2} = 32

7^{2 n + 1} \div 49 = 7^{3}

{(\frac{3}{2})}^{4} \times {(\frac{3}{2})}^{5} = {(\frac{3}{2})}^{2 n + 1}

{(\frac{2}{3})}^{10} + {\{{(\frac{3}{2})}^{2}\}}^{5} = {(\frac{2}{5})}^{2 n - 2}

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