Question

5 Raised to 3 ÷ 5 raised to 2m-1 = 1, then find m
${5}^{3} \div {5}^{2m - 1} = 1$

Answer 1

Answer :


$given \: equation \: = \: {5}^{3} \div {5}^{2m - 1} = 1 \\ \\ = > \: firstly \: calculate \: the \: quotient \: \\ \\ = > \: {5}^{3 - (2m - 1)} = 1 \\ \\ = > \: {5}^{3 - 2m - 1} = 1 \\ \\ = > \: {5}^{4 - 2m} = 1 \\ \\ = > \: {5}^{ - 2m + 4} = 1 \\ \\ = > \: write \: the \: no. \: in \: the \: exponental \: form \: with \: base \: 5 \\ \\ = > \: {5}^{ - 2m + 4} = {5}^{0} \\ \\ = > \: bases \: are \: same \: so \: exponents \: can \: be \: equal \\ \\ = > \: - 2m + 4 = 0 \\ \\ = > \: now \: find \: out \: the \: value \: of \: m \: \\ \\ = > \: - 2m = - 4 \\ \\ = > \: m = \frac{4}{2} \\ \\ = > \: m = 2$


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Answer 2

$\underline{\bold{Given:-}}$

${5}^{3} \div {5}^{2m - 1} = 1$

$\underline{\bold{To\:find:-}}$

Value of m.

$\underline{\bold{Solution:-}}$

${5}^{3} \div {5}^{2m - 1} = 1 \\ \\\bold{ When \: two \: numbers \: of \: same \: base \: are} \\ \bold{divided \: then \: there \: powers \: get} \\ \bold{subtracted. i.e.}\\ \bold{ {2}^{x} \div {2}^{y} = {2}^{x - y} }\\ \\ {5}^{3 - (2m - 1)} = 1 \\ \\ {5}^{4 - 2m} = {5}^{0 } \\ \\ \bold{They \: have \: same \: base \: so \: comparing} \\ \bold{there \: powers} \\ \\ 4 - 2m = 0 \\ \\ 4 = 2m \\ \\ m = \frac{4}{2} \\ \\ m = 2$

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