Question

Find the value of x if ,
${5}^{x - 3} \times {3}^{2x - 8} = 225$
$plz \: answer \: with \: correct \: explanation$
​

Answer 1

Explanation:

Given,

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

This can be written as

$5 {}^{x - 3} \times {3}^{2x - 8} = 25 \times 9$

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

Hence, we can conclude that

$x - 3 = 2x - 8 = 2$

Either can be taken for finding x.

$x - 3 = 2$

$x = 2 + 3 = 5$

OR

$2x - 8 = 2$

$2x = 2 + 8 = 10$

$x = \frac{10}{2} = 5$

Hence, x is equal to 5.

Answer: x=5

I hope this helps.

Answer 2

Step-by-step explanation:

5

x−3

×3

2x−8

=225

using \: a {}^{m + n} = a {}^{m} \times a {}^{n}usinga

m+n

=a

m

×a

n

5 {}^{x} \times 5 {}^{ - 3} \times 3 {}^{2x} \times 3 {}^{ - 8} = 2255

x

×5

−3

×3

2x

×3

−8

=225

5 {}^{x} \times \frac{1}{5 {}^{3} } \times 3 {}^{2x} \times \frac{1}{3 {}^{8} } = 2255

x

×

5

3

1

×3

2x

×

3

8

1

=225

5 {}^{x} \times \frac{1}{125} \times 3 {}^{2x} \times \frac{1}{6561}5

x

×

125

1

×3

2x

×

6561

1

5 {}^{x} \times \frac{1}{820125} \times 3 {}^{2x} = 2255

x

×

820125

1

×3

2x

=225

5 {}^{x} \times \frac{1}{820125} \times 9 {}^{x} = 2255

x

×

820125

1

×9

x

=225

(5 \times 9) {}^{x} = \frac{1}{820125} = 225(5×9)

x

=

820125

1

=225

45 {}^{x} \times \frac{1}{820125} = 22545

x

×

820125

1

=225

multiply both sides by 820125

820125 \times \frac{1}{820125} \times 45 {}^{x} = 820125 \times 225820125×

820125

1

×45

x

=820125×225

45 {}^{x} = 18452812545

x

=184528125

log_{45}(45 {}^{x} ) = log_{45}(184528125)log

45

(45

x

)=log

45

(184528125)

using \: log_{a}(a {}^{x} ) = xusinglog

a

(a

x

)=x

x = log_{45}(184528125)x=log

45

(184528125)

Alternative form (5)

P.S. : Point out mistakes if any! :p

Hope it helps!