If 5-m-2 - 5-4 - 5-3 - then m - nbsp-1-4-3

The correct option is D 3Note that for a nbsp;non zero integer a and integers m and n, a^m× a^n = a^m+n. ∴ 5^m+2× 5^4= 5^m+2+4 = 5^m+6 ⇒ 5^m+6= 5^3 Since the ...

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Standard VIII

Mathematics

Powers with like Bases

If 5^m+2 × 5^...

Question

If $5^{m + 2}$ $\times$ $5^{4}$ = $5^{3}$ , then $m$ = .

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Solution

The correct option is D -3
Note that for a non-zero integer $a$ and integers $m$ and $n$ ,
$a^{m} \times a^{n} = a^{m + n} .$
$∴ 5^{m + 2} \times 5^{4} = 5^{m + 2 + 4} = 5^{m + 6}$
$\Rightarrow 5^{m + 6} = 5^{3}$
Since the bases of powers on both sides of the equation are equal, the exponents can be equated.
$\Rightarrow m + 6 = 3$
$\Rightarrow m = - 3$

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Find the sum of the following series to infinity :

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(ii) $8 + 4 \sqrt{2} + 4 + . . . . \infty$

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(iv) 10 - 9 + 8.1 - 7.29 + ...... $\infty$

(v) $\frac{1}{3} + \frac{1}{5^{2}} + \frac{1}{3^{3}} + \frac{1}{5^{4}} + \frac{1}{3^{5}} + \frac{1}{5^{6}} + . . . . . \infty$

Q. If

5^{m + 2}

\times

5^{4}

5^{3}

, then

m

Q. If

5^{m + 2}

\times

5^{4}

5^{3}

, then

m

= .

Q. If

5^{m + 2}

\times

5^{4}

5^{3}

, then

m

= .

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

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If 5m+2 × 54 = 53 , then m = .

The correct option is D -3Note that for a non-zero integer a and integers m and n, am×an=am+n. ∴5m+2×54=5m+2+4=5m+6 ⇒5m+6=53 Since the bases of powers on both sides of the equation are equal, the exponents can be equated. ⇒m+6=3 ⇒m=−3

If $5^{m + 2}$ $\times$ $5^{4}$ = $5^{3}$ , then $m$ = .