Find the values of x in each of the following - iv 5x-2-32x-3-135

Given : nbsp;5^x 2×3^2x 3=135 nbsp;⇒ 5^x 2×3^2x 3=5^1×3^3 On comparing both the sides, we get x 2=1 and 2x 3=3 ⇒ x=2+1 and 2x=3+3 ⇒ x=3 and x=62=3 He ...

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Standard X

Mathematics

Discriminant

Find the valu...

Question

Find the values of x in each of the following :

iv) $5^{x - 2} \times 3^{2 x - 3} = 135$

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Solution

Given : $5^{x - 2} \times 3^{2 x - 3} = 135$

$\Rightarrow 5^{x - 2} \times 3^{2 x - 3} = 5^{1} \times 3^{3}$

On comparing both the sides, we get

$x - 2 = 1$ and $2 x - 3 = 3$

$\Rightarrow x = 2 + 1$ and $2 x = 3 + 3$

$\Rightarrow x = 3$ and $x = \frac{6}{2} = 3$

Hence, the value of $x = 3.$

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Similar questions

Find the values of x in each of the following:

$(i) 2^{5 x} \div 2^{x} = \sqrt[5]{2^{20}}$

$(i i) (2^{3})^{4} = (2^{2})^{x}$

$(i i i) {(\frac{3}{5})}^{x} {(\frac{5}{3})}^{2 x} = \frac{125}{27}$

$(i v) 5^{x - 2} \times 3^{2 x - 3} = 135$

$(v) 2^{x - 7} \times 5^{x - 4} = 1250$

$(v i) (\sqrt[3]{4})^{2 x + \frac{1}{2}} = \frac{1}{32}$

$(v i i) 5^{2 x + 3} = 1$

$(v i i i) (13)^{\sqrt{x}} = 4^{4} - 3^{4} - 6$

$(i x) {(\sqrt{\frac{3}{5}})}^{x + 1} = \frac{125}{27}$

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}

(iv)

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

(v)

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

Q. Find the values of x in each of the following:

(i)

2^{5 x} \div 2 x = \sqrt[5]{2^{20}}

(ii)

(2^{3})^{4} = (2^{2})^{x}

(iii)

{(\frac{3}{5})}^{x} {(\frac{5}{3})}^{2 x} = \frac{125}{27}

(iv)

5^{x - 2} \times 3^{2 x - 3} = 135

(v)

2^{x - 7} \times 5^{x - 4} = 1250

(vi)

{(\sqrt[3]{4})}^{2 x + \frac{1}{2}} = \frac{1}{32}

(vii)

5^{2 x + 3} = 1

(viii)

{(13)}^{\sqrt{x}} = 4^{4} - 3^{4} - 6

(ix)

{(\sqrt{\frac{3}{5}})}^{x + 1} = \frac{125}{27}

5^{x - y} . 3^{2 x - y} = 135

.Find the value of

x

and

y

Q. Find the value of x in the following:

(\frac{3}{5})^{x} . (\frac{5}{3})^{2 x} = \frac{125}{27}

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Discriminant

Standard X Mathematics

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Find the values of x in each of the following : iv) 5x−2×32x−3=135

Given : 5x−2×32x−3=135 ⇒ 5x−2×32x−3=51×33 On comparing both the sides, we get x−2=1 and 2x−3=3 ⇒ x=2+1 and 2x=3+3 ⇒ x=3 and x=62=3 Hence, the value of x=3.

Find the values of x in each of the following :

iv) $5^{x - 2} \times 3^{2 x - 3} = 135$

Given : $5^{x - 2} \times 3^{2 x - 3} = 135$

$\Rightarrow 5^{x - 2} \times 3^{2 x - 3} = 5^{1} \times 3^{3}$

On comparing both the sides, we get

$x - 2 = 1$ and $2 x - 3 = 3$

$\Rightarrow x = 2 + 1$ and $2 x = 3 + 3$

$\Rightarrow x = 3$ and $x = \frac{6}{2} = 3$

Hence, the value of $x = 3.$