If31- x - 5 y -452thenx -y -A- 3B- 2C- 1D- N

The correct options are A 3 B 2Given, nbsp;3^1+x× 5^y = 45^2 45 = 3× 15 = 3× 3× 5 = 3^2× 5 ∴45^2= nbsp; (3^2× 5)^2 =3^2× 2× 5^2 [(ab)^m = a^m× b^m ...

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Byju's Answer

Standard VII

Mathematics

Power Law of Exponent

If31+ x × 5 y...

Question

If
$3^{1 + x} \times 5^{y} = 45^{2}$
then
$x =$
$y =$

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Solution

The correct options are
A 3
B 2
Given, $3^{1 + x} \times 5^{y} = 45^{2}$

$45 = 3 \times 15 = 3 \times 3 \times 5 = 3^{2} \times 5$
$∴ 45^{2} = (3^{2} \times 5)^{2} = 3^{2 \times 2} \times 5^{2} [(a b)^{m} = a^{m} \times b^{m}; (a^{m})^{n} = a^{m} n] 3^{1 + x} \times 5^{y} = 3^{4} \times 5^{2}$

Compare the powers,
$∴ 1 + x = 4; y = 2 x = 4 - 1 = 3$

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If 31+x×5y=452 then x= y=

The correct options are A 3 B 2Given, 31+x×5y=452 45=3×15=3×3×5=32×5 ∴452=(32×5)2 =32×2×52 [(ab)m=am×bm; (am)n=amn]31+x×5y=34×52 Compare the powers, ∴1+x=4; y=2x=4−1=3

If
$3^{1 + x} \times 5^{y} = 45^{2}$
then
$x =$
$y =$