Question

if
$2 ^{n - 7} \times 5 ^{n - 4 } = 1250$
find the value of n

​

Answer 1

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\: {2}^{n - 7} \times {5}^{n - 4} = 1250$

Let make out the factors of 1250

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:1250 \:\:}}}\\ {\underline{\sf{5}}}& \underline{\sf{\:\:625 \:\:}} \\\underline{\sf{5}}&\underline{\sf{\:\:125\:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\:\:25 \:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\:\:5\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

So,

$\rm \implies\:1250 = 2 \times 5 \times 5 \times 5 \times 5$

$\rm \implies\:1250 = 2 \times {5}^{4}$

So,

$\rm :\longmapsto\: {2}^{n - 7} \times {5}^{n - 4} = 2 \times {5}^{4}$

$\rm :\longmapsto\: {2}^{n - 7} \times {5}^{n - 4} = {2}^{1} \times {5}^{4}$

So, on comparing, we get

$\rm :\longmapsto\:n - 7 = 1$

$\rm :\longmapsto\:n = 1 + 7$

$\bf\implies \:n = 8$

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MORE TO EXPLORE

$\boxed{\tt{ {x}^{m} \times {x}^{n} = {x}^{m + n} }}$

$\boxed{\tt{ {x}^{m} \div {x}^{n} = {x}^{m - n} }}$

$\boxed{\tt{ {( {x}^{m} )}^{n} = {x}^{mn} }}$

$\boxed{\tt{ {x}^{0} = 1 \: }}$

$\boxed{\tt{ {x}^{ - n} = \frac{1}{ {x}^{n} } \: }}$

Answer 2

Question:-

If

$\sf2 ^{n - 7} \times 5 ^{n - 4 } = 1250$ Find the value of n.

Given:-

$\sf2 ^{n - 7} \times 5 ^{n - 4 } = 1250$

To Find:-

• Value of n.

Solution:-

$\sf \: Since, given \: 2 ^{n - 7} \times 5 ^{n - 4 } = 1250.$

$\sf2 {}^{n - 7} \times 5 {}^{n - 4} = 2 \times 625 = 2 {}^{1} \times 5 {}^{4}$

Comparing power on both Sides.

$\sf2 {}^{n - 7} = 2 {}^{1} \: So,n - 7 = 1 \: = > n = 8.$

$\sf5 {}^{n - 4} = 5 {}^{4} \: So,n - 4 = 4 = > n = 8.$

So, n = 8.

Answer:-

Hence, the value of n = 8.

Hope you have satisfied. ⚘