Find the value of m such that 5m-2 - 54 - 53-

Given, 5^m+2 × 5^4=5^3 nbsp;5^(m+2)+4=5^3 nbsp; [∵ a^m × a^n=a^m+n] 5^m+6=5^3 Since the bases are same, hence equating the exponents, we get nbsp;m + 6 = ...

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Standard VIII

Mathematics

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Question

Find the value of $m$ such that $5^{m + 2}$ $\times$ $5^{4}$ = $5^{3}$ .

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Solution

Given, $5^{m + 2}$ $\times$ $5^{4} = 5^{3}$
$⟹ 5^{(m + 2) + 4} = 5^{3} [∵ a^{m} \times a^{n} = a^{m + n}]$
$⟹ 5^{m + 6} = 5^{3}$

Since the bases are same, hence equating the exponents, we get
$m + 6 = 3$
$\Rightarrow m = 3 - 6$
$∴ m = - 3$

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Find the value of m such that 5m+2 × 54 = 53.

Given, 5m+2 × 54=53 ⟹5(m+2)+4=53 [∵am×an=am+n] ⟹5m+6=53 Since the bases are same, hence equating the exponents, we get m+6=3 ⇒m=3−6 ∴m=−3

Find the value of $m$ such that $5^{m + 2}$ $\times$ $5^{4}$ = $5^{3}$ .

Given, $5^{m + 2}$ $\times$ $5^{4} = 5^{3}$
$⟹ 5^{(m + 2) + 4} = 5^{3} [∵ a^{m} \times a^{n} = a^{m + n}]$
$⟹ 5^{m + 6} = 5^{3}$

Since the bases are same, hence equating the exponents, we get
$m + 6 = 3$
$\Rightarrow m = 3 - 6$
$∴ m = - 3$