Question

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If 3^x= 5^y) = (75)^z, show that z = (2x + y)​

Answer 1

Answer:

3

x

=5

y

=75

z

3

x

=5

y

=75

z

=k

⇒3=k

x

1

,5=k

y

1

,75=k

z

1

5

2

×3=k

z

1

(k

y

1

)

2

×(k

x

1

)=k

z

1

By comparing powers

⇒

y

2

+

x

1

=

z

1

xy

2x+y

=

z

1

∴z=

2x+y

xy

[henceproved]

Explanation:

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Answer 2

Answer:

3^x =5^y = 5^2z × 3^z= k

3= k^1/x

5 = k^ 1/y

75= k^ 1/z

k^2/y × k ^ 1/x = k ^1/z

2/y+ 1/x = 1/z

2x+y/xy = 1/z

z = xy/ 2x+y

please let me know if it's correct or not in comments.