Find the value of x- if 5x-3- 32x-8-225-

Given equation can be rewritten as, 5^x 3× 3^2x 8=225 5^x 3× 3^2x 8=25× 9 5^x 3× 3^2x 8=5^2× 3^2 Now, on comparing LHS and RHS of the above equati ...

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Standard VIII

Mathematics

Comparison of Quantities Using Exponents

Find the valu...

Question

Find the value of $x,$ if $5^{x - 3} \times 3^{2 x - 8} = 225$ .

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Solution

Given equation can be rewritten as,
$5^{x - 3} \times 3^{2 x - 8} = 225$
$5^{x - 3} \times 3^{2 x - 8} = 25 \times 9$
$5^{x - 3} \times 3^{2 x - 8} = 5^{2} \times 3^{2}$

Now, on comparing LHS and RHS of the above equation we get,
$x - 3 = 2$ and $2 x - 8 = 2$

Both equations results $x = 5.$

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5^{x - 3} \times 3^{2 x - 8} = 225

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Q. Find the value of x in each of the following.

(i)

\sqrt[5]{5 x + 2} = 2

(ii)

\sqrt[3]{3 x - 2} = 4

(iii)

{(\frac{3}{4})}^{3} {(\frac{4}{3})}^{- 7} = {(\frac{3}{4})}^{2 x}

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5^{x - 3} \times 3^{2 x - 8} = 225

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\frac{3^{3 x} \cdot 3^{2 x}}{3^{x}} = \sqrt[4]{3^{20}}

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Find the value of x, if 5x−3×32x−8=225.

Given equation can be rewritten as,5x−3×32x−8=2255x−3×32x−8=25×95x−3×32x−8=52×32Now, on comparing LHS and RHS of the above equation we get,x−3=2 and 2x−8=2Both equations results x=5.

Find the value of $x,$ if $5^{x - 3} \times 3^{2 x - 8} = 225$ .

Given equation can be rewritten as,
$5^{x - 3} \times 3^{2 x - 8} = 225$
$5^{x - 3} \times 3^{2 x - 8} = 25 \times 9$
$5^{x - 3} \times 3^{2 x - 8} = 5^{2} \times 3^{2}$

Now, on comparing LHS and RHS of the above equation we get,
$x - 3 = 2$ and $2 x - 8 = 2$

Both equations results $x = 5.$