Math, asked by sharmadesraj1223, 2 days ago

*What will be the value of n in 27²ⁿ⁻¹ = (243)³?* 1️⃣ 3 2️⃣ 7 3️⃣ 9 4️⃣ 6​

Answers

Answered by tejt674
2

2n-1=3

2n=3+1

2n=4

n=4/2

n=2

Answered by pulakmath007
0

SOLUTION

TO CHOOSE THE CORRECT OPTION

The value of n in

 \sf{ {(27)}^{2n - 1} =  {(243)}^{3}  }

1️⃣ 3

2️⃣ 7

3️⃣ 9

4️⃣ 6

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that :

 \sf{1. \:  \:  {a}^{m}  \times  {a}^{n} =  {a}^{m + n}  }

 \displaystyle \sf{2. \:  \:  \:  \frac{ {a}^{m} }{ {a}^{n} }  =  {a}^{m - n} }

 \displaystyle \sf{3. \:  \:  \:  { ({a}^{m} )}^{n} =  {a}^{mn}  }

 \displaystyle \sf{4. \:  \:  {a}^{0}  = 1}

EVALUATION

Here the given equation is

 \sf{ {(27)}^{2n - 1} =  {(243)}^{3}  }

Now

 \sf{ {(27)}^{2n - 1} =  {(243)}^{3}  }

 \sf{ \implies {( {3}^{3} )}^{2n - 1} =  {( {3}^{5} )}^{3}  }

 \sf{ \implies {3}^{3(2n - 1)}  =  {3}^{5 \times 3} }

 \sf{ \implies {3}^{6n - 3}  =  {3}^{15} }

 \sf{ \implies 6n - 3 =  15}

 \sf{ \implies 6n  =  15 + 3}

 \sf{ \implies 6n  =  18}

 \sf{ \implies n  =  3}

FINAL ANSWER

Hence the correct option is 1️⃣ 3

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